ChemWiki - User contributions [en]

Rep:Mod:Wlt113

2017-02-24T06:53:22Z

Wlt113: /* Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion non-reacting atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity. The steric clash within the exo geometry also raises the energy of the exo product, leading to the endo product being the thermodynamically favoured one.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new2.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

An analysis of reactant FMO overlap has not been included in this Exercise: it is expected that similar overlaps exist here between the archetypal diene fragment and dienophile fragments, and secondary orbital and/or steric interactions in the transition state can be used to rationalize relative activation energies and whether the endo or exo Diels-Alder adduct is kinetically favoured. It is also expected that this system behaves like a normal electron-demand Diels-Alder reaction, considering that the diene has electron-donating alkyl substituents, whereas the dienophile contains electronegative oxygen atoms and electron-withdrawing S=O functioncal groups.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2 ('''Exercise 3'''), were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 ('''Exercise 1''' and '''3''') and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetically favoured endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

File:Wlt113 ex 2 exo MO sec int new2.png

2017-02-24T06:52:45Z

Wlt113:

File:Wlt113 ex 2 exo MO sec int new.png

2017-02-24T06:51:34Z

Wlt113: Wlt113 uploaded a new version of File:Wlt113 ex 2 exo MO sec int new.png

Rep:Mod:Wlt113

2017-02-24T06:46:48Z

Wlt113: /* Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity. The steric clash within the exo geometry also raises the energy of the exo product, leading to the endo product being the thermodynamically favoured one.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

An analysis of reactant FMO overlap has not been included in this Exercise: it is expected that similar overlaps exist here between the archetypal diene fragment and dienophile fragments, and secondary orbital and/or steric interactions in the transition state can be used to rationalize relative activation energies and whether the endo or exo Diels-Alder adduct is kinetically favoured. It is also expected that this system behaves like a normal electron-demand Diels-Alder reaction, considering that the diene has electron-donating alkyl substituents, whereas the dienophile contains electronegative oxygen atoms and electron-withdrawing S=O functioncal groups.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2 ('''Exercise 3'''), were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 ('''Exercise 1''' and '''3''') and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetically favoured endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:17:03Z

Wlt113: /* Reaction Scheme */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

An analysis of reactant FMO overlap has not been included in this Exercise: it is expected that similar overlaps exist here between the archetypal diene fragment and dienophile fragments, and secondary orbital and/or steric interactions in the transition state can be used to rationalize relative activation energies and whether the endo or exo Diels-Alder adduct is kinetically favoured. It is also expected that this system behaves like a normal electron-demand Diels-Alder reaction, considering that the diene has electron-donating alkyl substituents, whereas the dienophile contains electronegative oxygen atoms and electron-withdrawing S=O functioncal groups.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2 ('''Exercise 3'''), were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 ('''Exercise 1''' and '''3''') and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetically favoured endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:11:58Z

Wlt113: /* Conclusion */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2 ('''Exercise 3'''), were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 ('''Exercise 1''' and '''3''') and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetically favoured endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:09:25Z

Wlt113: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:08:20Z

Wlt113: /* Exercise 1: Reaction of Butadiene with Ethene */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:07:14Z

Wlt113: /* Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:06:26Z

Wlt113: /* Conclusion */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group ('''Exercise 3''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:04:48Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref> The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T06:04:09Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:56:54Z

Wlt113: /* Exercise 1: Reaction of Butadiene with Ethene */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="neutral"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:55:52Z

Wlt113: /* Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Butadiene and Ethene ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="1.1700243"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:51:54Z

Wlt113: /* Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions ('''Figure 3'''), which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref> Since there is significant overlap in both cases, this system may be considered an example of a neutral Diels-Alder reaction <ref name="1.1700243"> G. Hilt, K. I. Smolko, B. V. Lotsch, "Cobalt(I)-catalyzed Neutral Diels-Alder Reactions of Oxygen-functionalized Acyclic 1,3-Dienes with Alkynes", ''Synlett'', '''2002''', ''7'', 1081-1084.{{DOI|10.1063/1.1700243}}</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:36:31Z

Wlt113: /* Conclusion */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2'''). Finally, optimized transition state structures with different sites of reaction were obtained, and used to determine regioselectivity in a system with more than one diene functional group.

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:32:17Z

Wlt113: /* Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:31:39Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Energies (kJ mol-1) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:30:48Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies (EH), Activation Energies (kJ mol-1) and Reaction Enthalpies (kJ mol-1) for the Exo and Endo Adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ/mol) and Reaction Energies (kJ/mol) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:29:42Z

Wlt113: /* Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies, Activation energies and Reaction Enthalpies for the Exo and Endo Adducts (in kJ/mol), at 298 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ/mol) and Reaction Energies (kJ/mol) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:29:08Z

Wlt113: /* Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies, Activation energies and Reaction Enthalpies for the Exo and Endo Adducts (in kJ/mol), at 298 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Computed Energies (EH), Activation Energies (kJ/mol) and Reaction Energies (kJ/mol) for the Exo and Endo Diels-Alder, and Cheletropic reaction adducts, at 298.15 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:25:25Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product; this result is consistent with literature observations and computations.<ref name="chele">D. Suarez, T. L. Sordo, J. A. Sordo, "A Comparative Analysis of the Mechanisms of Cheletropic and Diels-Alder Reactions of 1,3-Dienes with Sulfur Dioxide: Kinetic and Thermodynamic Controls", ''J. Org. Chem.'', '''1995''', ''60'', 2848-2852.{{DOI|10.1021/jo00114a039}}</ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Computed Energies, Activation energies and Reaction Enthalpies for the Exo and Endo Adducts (in kJ/mol), at 298 K.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:20:47Z

Wlt113: /* Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in an alternative Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies. As shown in '''Table 9''', the kinetically favoured product is the endo product, and the thermodynamically favoured product is the exo product. However, the activation energies for both pathways are higher than their counterparts' in the previous Diels-Alder reaction, and the reaction enthalpies are both endothermic, as opposed to the exothermic reaction energies for the previous Diels-Alder reaction. Hence, this alternative Diels-Alder reaction is both kinetically and thermodynamically disfavoured with respect to the previous one discussed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:08:10Z

Wlt113: /* Visualization of Reaction Coordinate */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

The IRCs were calculated and illustrated for the exo and endo pathways of the expected Diels-Alder reaction, and the cheletropic reaction. As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:02:50Z

Wlt113: /* Variation in C-C Bond Lengths with Reaction Coordinate */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', which was obtained via an intrinsic reaction coordinate (IRC) calculation that is based on following the MEP from reactants to products. The computed C-C bond lengths within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T05:00:58Z

Wlt113: /* Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO+1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS LUMO+1.png|250px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS LUMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS LUMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 endo TS HOMO.png|250px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="background: #ffffff; color: white;" |[[File:Wlt113 ex 2 exo TS HOMO-1.png|300px|center]]
| style="background: #ffffff; color: white;" |[[File: Wlt113 ex 2 endo TS HOMO-1.png|250px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:58:00Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product. The reaction profile of all three pathways is illustrated in '''Figure 7'''.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:57:01Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 7''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:56:16Z

Wlt113: /* Visualization of Reaction Coordinate */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 6''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:54:51Z

Wlt113: /* Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Table 6''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 6''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:53:14Z

Wlt113: /* Kinetics and Thermodynamics of Reaction Pathways */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 5'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 7''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:52:22Z

Wlt113: /* Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 6'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 7''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:51:25Z

Wlt113: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 5''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 6'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 7''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 7: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:49:57Z

Wlt113: /* Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 4''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:48:06Z

Wlt113: /* Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 6'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 6''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:46:57Z

Wlt113: /* Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 5'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:46:04Z

Wlt113: /* Reaction Scheme */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:45:03Z

Wlt113: /* Visualization of Reaction Coordinate */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 5''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 5''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:44:26Z

Wlt113: /* Visualization of Reaction Coordinate */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in '''Figure 4''', corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:42:39Z

Wlt113: /* Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x400px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO-1'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:40:36Z

Wlt113: /* Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center; background: #ffffff;"|''' LUMO+1 '''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| style="text-align: center; background: #ffffff;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 19; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''LUMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 18; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center; background: #ffffff;"|'''HOMO'''
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| style="text-align: center; background: #ffffff;"|[[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 17; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:32:24Z

Wlt113: /* Introduction */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain.<ref name="10.1146/annurev.pc.32.100181.001111"> P. Pechukas, "Transition state theory.", ''Annual Review of Physical Chemistry'', '''1981''', ''32'', 159-177.{{DOI|10.1146/annurev.pc.32.100181.001111}}</ref> Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot.<ref name="10.1146/annurev.pc.32.100181.001111"></ref> The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products.<ref name="10.1146/annurev.pc.32.100181.001111"></ref>

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d),<ref name="10.1063/1.464304"> A. D. Becke, "A new mixing of Hartree–Fock and local density‐functional theories", ''J. Chem. Phy.'', '''1993''', ''98'', 1372.{{DOI|10.1063/1.464304}}</ref> the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS HOMO transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T04:24:46Z

Wlt113: /* Introduction */

== Introduction ==

Much of chemical kinetics today is fundamentally based upon transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can attain. (REF) Mathematically, it is a type of stationary point, and as shown in '''Figure 1''', can appear as either a maximum point in a 1-dimensional (1D) plot, or a saddle point in a 2-dimensional potential energy surface (PES) plot. The saddle point in the 2D PES divides the stable potential wells of the reactants and products, and represents a dividing surface where there is only one direction to proceed in without elevating the system's energy. (REF) In addition, the reaction coordinate taken in the 1D plot often represents the minimum energy path (MEP) in the 2D PES leading from the reactants to the products

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref name="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://211.81.50.59//education/OCPkb/module2.php </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|500px|center]]
| [[File:Potential energy surface.jpg|300px|center]]
|}

Using computational methods, it is possible to calculate and compare the energies of the reactants, transition state and products, and assess the reactivity of various pathways for a reaction by comparing activation energies and reaction free energy changes or reaction energies. In this work, using the computational software Gaussian at the semi-empirical PM6 and hybrid functional density functional theory (DFT) method B3LYp/6-31G(d), the transition states of several Diels-Alder reactions are investigated to shed insight on the kinetics and thermodynamics of the pathways possible, taking into account stereoelectronic effects where relevant.

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS HOMO transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T03:59:01Z

Wlt113: /* Introduction */

== Introduction ==

Much of chemical kinetics today depends on the transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can enter. Mathematically, it is a type of stationary point, and as shown in Figure 1, can appear as In this work, using the computational software Gaussian, the transition states of several Diels-Alder reactions are investigated to shed insight on the reaction mechanism, and the effects of stereoelectronics are elucidated where relevant.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 1: ('''a''') 1D Reaction Profile and ('''b''') 2D PES.<ref="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://www.ch.ic.ac.uk/motm/porphyrins/images/saddle.gif </ref>
! style="background: #0D4F8B; color: white;" | ('''a''')
! style="background: #0D4F8B; color: white;" | ('''b''')
|-
| [[File:Wlt113 intro rexn profile.png|400px|center]]
| [[File:PES.gif|400px|center]]
|}

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS HOMO transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

Rep:Mod:Wlt113

2017-02-24T03:50:44Z

Wlt113: /* Introduction */

== Introduction ==

Much of chemical kinetics today depends on the transition state theory (TST), which postulates that the transition state is a theoretical high-energy state that reacting molecules can enter. Mathematically, it is a type of stationary point, and as shown in Figure 1, can appear as In this work, using the computational software Gaussian, the transition states of several Diels-Alder reactions are investigated to shed insight on the reaction mechanism, and the effects of stereoelectronics are elucidated where relevant.

Figure 1: (a) 1D Reaction Profile and (b) 2D Potential Energy Surface (PES).<ref="2D_PES">"2-Dimensional Potential Energy Surface." Taken from: http://www.ch.ic.ac.uk/motm/porphyrins/images/saddle.gif </ref>

[[File:Wlt113 intro rexn profile.png|400px|center|thumb|

{| class="wikitable"
! style="background: #0D4F8B; color: white;" | Column 1, Row 1
! style="background: #0D4F8B; color: white;" | Column 2, Row 1
! style="background: #0D4F8B; color: white;" | Column 3, Row 1
|-
| Column 1, Row 2
| Column 2, Row 2
| Column 3, Row 2
|-
| Column 1, Row 3
| Column 2, Row 3
| Column 3, Row 3
|}

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS HOMO transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />

File:Wlt113 intro rexn profile.png

2017-02-24T03:49:06Z

Wlt113:

Rep:Mod:Wlt113

2017-02-24T03:31:17Z

Wlt113: /* Introduction */

== Introduction ==

In chemical reactions, the transition state is a theoretical high-energy electronic state inhabited by the activated complex, a transient species formed from reacting molecules. Mathematically, it is a type of stationary point, and as shown in Scheme ??, can appear as In this work, using the computational software Gaussian, the transition states of several Diels-Alder reactions are investigated to shed insight on the reaction mechanism, and the effects of stereoelectronics are elucidated where relevant.

Figure 1: (a) 1D Reaction Profile and (b) 2D Potential Energy Surface (PES).

== Exercise 1: Reaction of Butadiene with Ethene ==

=== Reaction Scheme ===

[[File:wlt113_Ex 1 Scheme corrected.png|400px|center]]

In this exercise, the Diels-Alder cycloaddition between butadiene and ethene was studied, and the transition state optimized using Gaussian at the PM6 level. Links to the calculation output for the optimized structures of butadiene,<ref name="PM6_opt_butadiene">"PM6-optimized Structure of Butadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_BUTADIENE_MOS_OPT.LOG</ref> ethene,<ref name="PM6_opt_ethene">"PM6-optimized Structure of Ethene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_ETHENE_MOS_OPT.LOG</ref> cyclohexene,<ref name="PM6_opt_cyclohexene">"PM6-optimized Structure of Cyclohexene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_OPT.LOG</ref> the transition state,<ref name="PM6_opt_ex 1_TS">"PM6-optimized Transition State Structure for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</ref> and the intrinsic reaction coordinate (IRC)<ref name="PM6_IRC_ex 1">"Intrinsic Reaction Coordinate (IRC) for Exercise 1." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_IRC.LOG</ref> can be found in '''References'''.

=== Orbital Symmetry-controlled Overlap of Frontier MOs of Cyclohexadiene and 1,3-Dioxole ===

The reactivity of the reactants in a Diels-Alder cycloaddition can be rationalized using frontier molecular orbital (FMO) theory.<ref name="1.1700243"> K. Fukui, T. Yonezawa, and H. Shingu, "Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons", ''J. Chem. Phy.'', '''1952''', ''20'', 722.{{DOI|10.1063/1.1700243}}</ref> As shown in '''Figure 2''', the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of ethene and butadiene can overlap to form key FMOs in the transition state and resultant cyclohexene product. An MO can be symmetric (having a plane of symmetry) or antisymmetric (lacking a plane of symmetry), and as shown in the MO diagram, the symmetry requirements in such a reaction are that reactant MOs of the same symmetry must interact for the orbital overlap to be non-zero. The overlap integrals for the three possible cases where reactant MOs can be either symmetric or antisymmetric are shown below ('''Table 2'''). These results are consistent with the Woodward-Hoffmann rules for pericyclic reactions, which predicts that the reaction is thermally allowed whether the HOMO of butadiene overlaps with the LUMO of ethene (normal electron-demand Diels-Alder reaction) or the HOMO of ethene overlaps with the LUMO of butadiene (inverse electron-demand).<ref name=""> F. A. Carey, R. J. Sundberg. (2007). "Advanced Organic Chemistry: Part A: Structures and Mechanisms (5th ed.)", New York: Springer. ISBN 978-0-387-44899-2</ref>

[[File:Wlt113_ex_1_MO_w_Gaussian corrected 2.png|800px|center|thumb|white|'''Figure 2''': MO diagram showing overlap of FMOs of Ethene and Butadiene to form FMOs in the Diels-Alder transition state (shown in '''Table 1'''). MOs can be either symmetric ('''S''') or asymmetric ('''AS''').]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: FMOs of the Diels-Alder Transition State between Butadiene and Ethene. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |''' LUMO+1 '''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 1 butadiene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene LUMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS LUMO+1 transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 1 butadiene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 ethene HOMO transparent.png|x200px|center]]
| [[File:Wlt113 ex 1 TS HOMO transparent.png|x200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| style="text-align: center;"| '''N.A.'''
| style="text-align: center;"| '''N.A.'''
| <jmol><jmolApplet><uploadedFileContents>WLT_EXERCISE_1_CYCLOHEXENE_FROZEN_TS_MOS_OPT.LOG</uploadedFileContents><color>white</color><script>frame 6; rotate z -90; mo 16; mo nodots nomesh fill translucent; mo titleformat "",</script></jmolApplet></jmol>
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Overlap Integrals for Interaction of Symmetric and/or Antisymmetric Reactant MOs
! style="background: #0D4F8B; color: white;" | Symmetries of Reactant MOs
! style="background: #0D4F8B; color: white;" | Overlap Integral
! style="background: #0D4F8B; color: white;" | Reaction allowed?
|-
| style="text-align: center;" |'''Symmetric-Symmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
| style="text-align: center;" |'''Symmetric-Antisymmetric'''
| style="text-align: center;" |Zero
| style="text-align: center;" |Forbidden
|-
| style="text-align: center;" |'''Antisymmetric-Antisymmetric'''
| style="text-align: center;" |Non-zero
| style="text-align: center;" |Allowed
|-
|}

[[File:Wlt113_WH_rules.png|center|thumb|'''Figure 3''': Suprafacial-suprafacial overlap of ('''a''') the HOMO of Butadiene with the LUMO of Ethene, and; ('''b''') the HOMO of Ethene with the LUMO of Butadiene ]]

=== Variation in C-C Bond Lengths with Reaction Coordinate ===

The lengths of the C-C bonds within reactant molecules vary continuously with reaction coordinate, as shown in '''Figure 4''', and their computed values within the reactants, transition state and product are tabulated in '''Table 3'''.

The C1-C6 and C4-C5 bonds (1.33 Å) are initially slightly shorter than the typical sp2-sp2 C=C double bond length (1.34 Å) in butadiene, due to π-conjugation, but subsequently surpasses 1.34 Å and increases to 1.37 Å in the transition state, ultimately becoming single bonds (1.50 Å) in the cyclohexene product with the typical sp2-sp3 C-C bond length (1.50 Å).<ref name="Clayden"> J. Clayden, N. Greeves, S. Warren, P. Wothers. (2001). "Organic Chemistry (2nd ed.)", OUP Oxford. ISBN 978-0-19-927029-3</ref> The C4-C5 bond is initially a typical sp2-sp2 C-C bond (1.47 Å), but decreases in length in the transition state (1.41 Å), until it reaches a typical sp2-sp2 C=C bond.<ref name="Clayden"></ref>

The C2-C3 C=C bond in ethene (1.33 Å) is slightly shorter than the typical sp2-sp2 C=C bond length; as the reaction progresses, it lenghthens to being intermediate to typical sp2-sp2 and sp3-sp3 C-C bond lengths (1.38 Å), and eventually becomes a typical sp3-sp3 C-C bond.<ref name="Clayden"></ref>

Within the transition state, the C1-C2 and C3-C4 bond length of 2.11 Å is intermediate between a typical sp3-sp3 C-C bond (1.54 Å)<ref name="Clayden"></ref> and the sum of Van der Waals (VDW) radii for two carbon atoms (3.40 Å).<ref name="10.1023/A:1011625728803"> S. S. Batsanov. "Van der Waals Radii of Elements", ''Inorganic Materials'', '''2001''', ''37'', 871-885.{{DOI|10.1023/A:1011625728803}}</ref> The distance between two atoms being under the sum of their VDW radii is the indication of a bonding interaction, which is the case of the two partially formed C1-C2/C3-C4 bonds in the transition state.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: C-C Bond Distances in the Butadiene and Ethene Reactants, the Transition State, and the Cyclohexene Product. ('''N.A.''' = Not Applicable.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethene
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #0D4F8B; color: white;" | Cyclohexene
|-
| style="text-align: center;" |'''C1-C2'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C2-C3'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.33
| style="text-align: center;" |1.38
| style="text-align: center;" |1.53
|-
| style="text-align: center;" |'''C3-C4'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |2.11
| style="text-align: center;" |1.54
|-
| style="text-align: center;" |'''C4-C5'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
| style="text-align: center;" |'''C5-C6'''
| style="text-align: center;" |1.47
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.41
| style="text-align: center;" |1.34
|-
| style="text-align: center;" |'''C1-C6'''
| style="text-align: center;" |1.33
| style="text-align: center;" |'''N.A.'''
| style="text-align: center;" |1.38
| style="text-align: center;" |1.50
|-
|}

[[File:Wlt113 ex 1 IRC C-C bond distance.png|700px|center|thumb|white|'''Figure 4''': Plot showing Variation in C-C Bond Distances with Reaction Coordinate.]]

=== Visualization of Reaction Coordinate ===

As shown in Figure 4, corresponding to the vibration with an imaginary frequency of 948.83i cm-1, formation of the two C-C bonds between butadiene and ethene in the transition state is a synchronous and concerted process, as expected for the symmetrical system where two equivalent C-C bonds are formed.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 3''': Front and Side Views of the Vibration corresponding to the Reaction Path at the Transition State.
! style="background: #0D4F8B; color: white;" | Front View
! style="background: #0D4F8B; color: white;" | Side View
|-
| [[File:wlt113 ex 1 TS vib front view.gif|500px|center]]
| [[File:wlt113 ex 1 TS vib side view.gif|500px|center]]
|-
|}

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==

=== Reaction Scheme ===

[[File:wlt113_Ex 2 Scheme.png|500px|center|thumb|'''Scheme 2''': The Diels-Alder reaction of Cyclohexadiene and 1,3-Dioxole to form the (i) exo or (ii) endo cycloaddition product]]

In this exercise, the Diels-Alder reaction between the electron-rich dienophile 1,3-dioxole and the diene cyclohexadiene was studied, and the transition state was initially optimized at PM6, before being reoptimized at the B3LYP/6-31G(d) level of theory. Links to the calculation output for the PM6 and B3LYP/6-31G(d)-optimized structures of cyclohexadiene,<ref name="PM6_opt_cyclohexadiene">"PM6-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_cyclohexadiene">"B3LYP/6-31G(d)-optimized Structure of Cyclohexadiene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_CYCLOHEXADIENE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> 1,3-dioxole,<ref name="PM6_opt_1,3-dioxole">"PM6-optimized Structure of 1,3-Dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_1,3-dioxole">"B3LYP/6-31G(d)-optimized Structure of 1,3-dioxole." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_DIOXOLE_REACTANT_SYMMETRY_BROKEN_B3LYP_6-31G(D)_OPT.LOG</ref> the exo product,<ref name="PM6_opt_exo pdt_ex 2">"PM6-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Exo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the endo product,<ref name="PM6_opt_endo pdt_ex 2">"PM6-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo pdt_ex 2">"B3LYP/6-31G(d)-optimized Structure of the Endo Product for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_B3LYP_6-31G(D)_OPT.LOG</ref> the exo transition state,<ref name="PM6_opt_exo TS_ex 2">"PM6-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_exo TS_ex 2">"B3LYP/6-31G(d)-optimized Exo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> the endo transition state,<ref name="PM6_opt_endo_TS_ex 2">"PM6-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_OPT.LOG</ref> <ref name="B3LYP/6-31G(d)_opt_endo TS_ex 2">"B3LYP/6-31G(d)-optimized Endo Transition State Structure for Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:Wlt_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_MO_opt.log</ref> and the intrinsic reaction coordinate (IRC) of the exo pathway<ref name="PM6_exo_IRC_ex 2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_EXO_PRODUCT_FROZEN_TS_IRC_RECORRECT_NEVER.LOG</ref> <ref name="B3LYP/6-31G(d)_exo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for Exo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_exo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> and endo pathway<ref name="PM6_endo TS IRC_ex2">"PM6-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_2_ENDO_PRODUCT_FROZEN_TS_IRC.LOG</ref><ref name="B3LYP/6-31G(d)_endo IRC_ex 2">"B3LYP/6-31G(d)-optimized Intrinsic Reaction Coordinate (IRC) for the Endo Transition State in Exercise 2." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_exercise_2_endo_product_frozen_TS_B3LYP_6-31G(d)_IRC.log</ref> can be found in '''References'''.

=== Overlap of FMOs of Cyclohexadiene and 1,3-Dioxole ===

The orbital symmetry-controlled overlap of reactant FMOs are shown in '''Figure 4'''. This is an example of an inverse electron-demand Diels-Alder reaction as the HOMO in the system is that of the 1,3-dioxole dienophile, whereas the LUMO is contributed by cyclohexadiene.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 4''': MO diagram showing overlap of FMOs of 1,3-Dioxole and Cyclohexadiene to form FMOs in the exo and endo Diels-Alder transition state (shown in '''Table 3''').
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| [[File:Wlt113 ex 2 exo MO w Gaussian new.png|500px|center]]
| [[File:Wlt113 ex 2 endo MO w Gaussian new.png|500px|center]]
|-
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: FMOs of the ('''a''') exo and ('''b''') endo Diels-Alder Transition State between 1,3-Dioxole and Cyclohexadiene
! style="background: #0D4F8B; color: white;" | MO
! style="background: #0D4F8B; color: white;" | Graphic Representation of exo MOs
! style="background: #0D4F8B; color: white;" | Graphic Representation of endo MOs
|-
| style="text-align: center;" |''' LUMO+1 '''
| [[File:Wlt113 ex 2 exo TS LUMO+1.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS LUMO+1.png|200px|center]]
|-
| style="text-align: center;" |'''LUMO'''
| [[File:Wlt113 ex 2 exo TS LUMO.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS LUMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO'''
| [[File:Wlt113 ex 2 exo TS HOMO.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO.png|200px|center]]
|-
| style="text-align: center;" |'''HOMO-1'''
| [[File:Wlt113 ex 2 exo TS HOMO-1.png|200px|center]]
| [[File: Wlt113 ex 2 endo TS HOMO-1.png|200px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

The activation energies and reaction enthalpies for the formation of the exo and endo adducts respectively were calculated by taking differences in the values of ''Sum of electronic and thermal Free energy'' obtained for the reactants, transition state and products through Gaussian ('''Table 4'''). It was found that the endo product was both the kinetically (lower activation energy) and thermodynamically (larger, more negative reaction enthalpy) favoured product, as compared to the exo product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Activation energies and reaction enthalpies for the exo and endo adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan="3" style="text-align: center; background: white;" | '''Reactants'''
| style="text-align: center; background: white;" | '''Cyclohexadiene'''
| style="text-align: center; background: white;" | -233.324375
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
|-
| style="text-align: center; background: white;" | '''1,3-Dioxole'''
| style="text-align: center; background: white;" | -267.068643
|-
| style="text-align: center; background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | -500.393018
|-
| rowspan="2" style="text-align: center; background: white;" | '''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.285411
| style="text-align: center; background: white;" | 282.52
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.332149
| style="text-align: center; background: white;" | 159.81
|-
| rowspan="2" style="text-align: center; background: white;" | '''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | -500.417322
| rowspan="3" style="text-align: center; background: white;" |'''N.A.'''
| style="text-align: center; background: white;" | -63.81
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | -500.418692
| style="text-align: center; background: white;" | -67.41
|}

=== Secondary Orbital Interactions and Steric Factors influencing Stereoselectivity in the Transition State ===

The lower activation energy for endo product formation can be explained by secondary orbital interactions. As shown in '''Figure 5''', the p-orbital coefficients on the oxygen atoms are of the correct phase to and can overlap with the orbital coefficients on the diene carbon atoms not directly involved in bond formation. In addition, in the exo transition state, the steric repulsion between H atoms of the reactants (as illustrated in '''Table 4''') is destabilizing. Hence, both electronic and steric factors favour the endo transition state, leading to the computed kinetic and thermodynamic stereoselectivity.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Primary and Secondary Orbital Interactions between 1,3-Dioxole and Cyclohexadiene in the Diels-Alder Transition State. (Primary bonding interactions are shown as black dashed lines, whereas secondary orbital interactions are shown as red dashed lines.)
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
| style="text-align: center;" |''' MO Graphic '''
| [[File:Wlt113 ex 2 exo MO sec int new.png|200px|center]]
| [[File:Wlt113 ex 2 endo MO sec int.png|200px|center]]
|-
| style="text-align: center;" |'''Computed MO'''
| [[File:Wlt113 ex 2 exo TS HOMO iso 001.png|200px|center]]
| [[File:Wlt113 ex 2 endo TS HOMO iso 001.png|200px|center]]
|-
|}

== Exercise 3: Comparing the Diels-Alder and Cheletropic Reactions between o-Xylylene and SO2 ==

=== Reaction Scheme ===

[[File:Wlt113 Ex 3 Scheme new.png|700px|center]]

In this final exercise, the expected exo and endo hetero-Diels-Alder reaction pathways, the alternative exo and endo Diels-Alder reaction, and the cheletropic reaction pathway between the electron-deficient dienophile SO2 and the electron-rich diene o-xylylene are compared by optimization of the corresponding reactants, transition states and products at the PM6 level. Links to the calculation output for the optimized structures of o-xylylene,
<ref name="PM6_opt_o-xylylene">"PM6-optimized Structure of o-Xylylene." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_DIENE_REACTANT_OPT.LOG</ref> SO2,
<ref name="PM6_opt_SO2">"PM6-optimized Structure of Sulfur Dioxide." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_SO2_REACTANT_OPT.LOG</ref> the exo,<ref name="PM6_opt_exo_normal DA_ex 3">"PM6-optimized Structure of the Exo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_OPT.LOG</ref> and endo<ref name="PM6_opt_endo_normal DA_ex 3">"PM6-optimized Structure of the Endo Product from the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_ENDO_PRODUCT_OPT.LOG</ref> product for the expected Diels-Alder reaction, the cheletropic product,<ref name="PM6_opt_cheletropic_ex 3">"PM6-optimized Structure of the Cheletropic Product for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_PRODUCT_OPT.LOG</ref> the exo,
<ref name="PM6_opt_exo_other DA_ex 3">"PM6-optimized Structure of the Exo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_PRODUCT_OPT.LOG</ref> and endo product
<ref name="PM6_opt_endo_other DA_ex 3">"PM6-optimized Structure of the Endo Product from the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_PRODUCT_OPT.LOG</ref> for the alternative Diels-Alder reaction, the exo
<ref name="PM6_opt_exo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE-SO2_FROZEN_TS_OPT.LOG</ref> and endo
<ref name="PM6_opt_endo_TS_normal DA_ex 3">"PM6-optimized Transition State Structure of the Endo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition state for the expected Diels-Alder reaction, the cheletropic transition state,<ref name="PM6_opt_cheletropic_TS_ex 3">"PM6-optimized Transition State Structure of the Cheletropic Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_OPT.LOG</ref> the exo<ref name="PM6_opt_exo TS_other DA_ex3">"PM6-optimized Exo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_EXO_POSTFROZEN_TS_OPT.LOG</ref> and endo<ref name="PM6_opt_endo TS_other DA_ex3e">"PM6-optimized Endo Transition State Structure of the Alternative Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_OTHER_DA_ENDO_POSTFROZEN_TS_OPT.LOG</ref> transition states for the alternative Diels-Alder reaction, and the intrinsic reaction coordinate (IRC) of the exo<ref name="PM6_exo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_TUTORIAL_METHOD_3_XYLYLENE_SO2_TS_IRC.LOG</ref> and endo<ref name="PM6_IRC_endo_normal DA_ex 1">"Intrinsic Reaction Coordinate (IRC) of the Exo Pathway of the Expected Diels-Alder Reaction for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_XYLELENE-SO2_ENDO_POSTFROZEN_TS_IRC.LOG</ref> pathways of the expected Diels-Alder reaction, and the cheletropic<ref name="PM6_IRC_cheletropic_ex 3">"Intrinsic Reaction Coordinate (IRC) of the Cheletropic Reaction Pathway for Exercise 3." https://wiki.ch.ic.ac.uk/wiki/index.php?title=File:WLT_EXERCISE_3_CHELETROPIC_FROZEN_TS_IRC.LOG</ref> pathway can be found in '''References'''.

=== Visualization of Reaction Coordinate ===

As shown in '''Table 5''', the formation of two new bonds is asynchronous with both Diels-Alder reactions (with formation of the C-O bond slightly faster than that of the C-S bond), but synchronous in the cheletropic reaction (where both C-S bonds form simultaneously). In addition, the o-xylylene fragment appears to aromatize and form an aromatic 6-membered ring with delocalization extending to the carbon atoms outside the ring, which suggests that o-xylylene reacts as a diradical in the transition state. This would be due to the aromatic driving force and the inherent instability of o-xylylene.

(Define IRC near the top)

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Illustration of Bond Formation in the Transition State and Plot of Energy against IRC for the formation of the ('''a''') exo and ('''b''') endo Diels-Alder adducts and ('''c''') the Cheletropic adduct.
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | (a) Exo
! style="background: #0D4F8B; color: white;" | (b) Endo
! style="background: #0D4F8B; color: white;" | (c) Cheletropic
|-
| style="text-align: center;" |'''Illustration of Bond Formation'''
| style="background: #787bd3; colour: white;" |[[File:Wlt113 ex 3 exo IRC movie new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_endo_IRC_movie_new.gif|300px|center]]
| style="background: #787bd3; colour: white;" |[[File:Wlt113_ex_3_cheletropic_IRC_movie_new.gif|300px|center]]
|-
| style="text-align: center;" |'''Plot of Energy against IRC '''
| style="background: #ffffff; colour: white;" |[[File:Ex 3 exo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 endo IRC plot.png|300px|center]]
| style="background: #ffffff; colour: white;" |[[File:Ex 3 cheletropic IRC plot new.png|300px|center]]
|-
|}

=== Kinetics and Thermodynamics of Reaction Pathways ===

(Define Diels-Alder as DA near the top)

Analysis of activation energies and reaction energies ('''Table 6''') revealed that for the expected Diels-Alder reaction, the endo product is the kinetic product and the exo product is the thermodynamic product, but overall, taking the chelotropic reaction into account, the chelotropic product is the thermodynamically favoured product (largest, most negative reaction energy) whereas the endo Diels-Alder product is the kinetic product (lowest activation energy). This suggests that if a mixture of o-xylylene and SO2 were allowed to react, the endo Diels-Alder product would be the fastest-formed, but if left to equilibrate, the product mixture will feature the cheletropic adduct as the major product.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6: Activation energies and reaction energies for the exo and endo Diels-Alder, and cheletropic reaction adducts (in kJ/mol)
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "3" style="text-align: center" |'''Reactants'''
| style="text-align: center; background: white;" | '''o-Xylylene'''
| style="text-align: center; background: white;" | 0.178746
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''SO2'''
| style="text-align: center; background: white;" | -0.118614
|-
| style="text-align: center;"background: white;" | '''Sum of Reactant Energies'''
| style="text-align: center; background: white;" | 0.060132
|-
| rowspan="3" style="text-align: center;|'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.092077
| style="text-align: center; background: white;" | 83.87
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.090559
| style="text-align: center; background: white;" | 79.89
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | 0.099062
| style="text-align: center; background: white;" | 102.21
|-
| rowspan="3" style="text-align: center; |'''Product'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.021454
| rowspan="3" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" | -101.55
|-
| style="text-align: center; background: white;" | '''Endo'''
| style="text-align: center; background: white;" | 0.021696
| style="text-align: center; background: white;" | -100.91
|-
| style="text-align: center; background: white;" | '''Cheletropic'''
| style="text-align: center; background: white;" | -0.000001
| style="text-align: center; background: white;" | -157.88
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ '''Figure 7''': Reaction Profile Diagram for the Three Possible Reaction Pathways.
|[[File:Ex 3 reaction pathway.png|600px|center]]
|}

=== Diels-Alder Cycloaddition involving an Alternative Diene in o-Xylylene ===

As indicated in the Reaction Scheme, o-Xylylene contains a second diene fragment in an s-cis configuration, and the reactivity of this fragment in a Diels-Alder reaction via the exo and endo pathways was examined by computation of the corresponding activation energies and reaction energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 9: Computed Energies (EH), Activation energies (kJ/mol) and Reaction Energies (kJ/mol) for the AlternativeExo and Endo Diels-Alder Reaction Pathways.
! colspan="2" style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Computed Energy of Species (EH)
! style="background: #0D4F8B; color: white;" | Activation Energy (kJ mol-1)
! style="background: #0D4F8B; color: white;" | Reaction Energy (kJ mol-1)
|-
| rowspan= "2" style="text-align: center" |'''Transition State'''
| style="text-align: center; background: white;" | '''Exo'''
| style="text-align: center; background: white;" | 0.105057
| style="text-align: center; background: white;" |117.95
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.102071
| style="text-align: center; background: white;" |110.11
|-
| rowspan= "2" style="text-align: center" |'''Product'''
| style="text-align: center; background: white;" |'''Exo'''
| style="text-align: center; background: white;" |0.067304
| rowspan="2" style="text-align: center; background: white;" | '''N.A.'''
| style="text-align: center; background: white;" |18.83
|-
| style="text-align: center; background: white;" |'''Endo'''
| style="text-align: center; background: white;" |0.065609
| style="text-align: center; background: white;" |14.38
|-
|}

== Conclusion ==

In conclusion, the reactivity of the Diels-Alder reactions between the diene/dienophile systems, butadiene/ethene ('''Exercise 1'''), cyclohexadiene/1,3-dioxole ('''Exercise 2'''), and o-xylylene/SO2, were investigated via calculations on Gaussian software, and the reactants, transition state structures and products were optimized at PM6 (Exercise 1 and 3) and B3LYP/6-31G(d) ('''Exercise 2''') levels of theory. In each case, IRC calculations were used to illustrate the reaction coordinate, and the type of Diels-Alder reaction (normal or inverse electron-demand) was determined from analysis of overlapping reactant FMOs. The activation energies and reaction energies were calculated to establish the kinetically and thermodynamically favoured reaction pathways, and the involvement of secondary orbital interactions and sterics was used to explain the lower activation energy for the formation of the kinetic endo product for the cyclohexadiene/1,3-dioxole system ('''Exercise 2''').

== References ==

<references />