Sl8514:

== Introduction ==

[[File:Sl8514_reaction_profile.png|400px|thumb|Fig. 1 2D Reaction Energy Profile]]
[[File:Sl8514_potential_energy_surface.gif|400px|thumb|Fig. 2 Potential Energy Surface. Saddle point - Transition state, linking a local minimum and a global minimum]]
=== Chemical Reactions and Potential Energy Surfaces ===

In a conventional 2D reaction energy profile (Fig. 1), one can imagine the transition state as a structure with maximum free energy linking the two minima that represent the reactants and products. However, in chemical systems of interest, there are usually more than one degrees of freedom in the reaction that can serve as the reaction coordinate, requiring a higher-dimensional plot that captures all the degrees of freedom involved in an reaction.

This is the potential energy surface, which is an important concept in Computational Chemistry and reaction modeling. As the potential energy surface can be seen as a higher-dimension extension of the 2D reaction profile, the same principles apply - reactants and products represent minima on the potential energy surface, and transition states are maxima that links two minima together. Due to the increased number of dimensions, the definition of transition states must be further refined as a ''first-order saddle point'' on the potential energy surface (Fig. 2). This means that it must be a minima in any other direction except for the direction of the reactant coordinate, ensuring the presence of a lower-energy "channel" (see Fig. 2) where the molecule must flow through. In quantum mechanical simulations, minima are defined by having positive second derivatives of the Hessian in every direction, while first-order saddle points are defined by having positive second derivatives in every direction except for the direction of the reaction coordinate, where the derivative is positive.

In calculations by the Gaussian software package, frequency analysis allows definitive determination of the transition state by affording a negative vibrational mode on transition state structures that traces the predicted path of the reaction.

=== Diels-Alder Reactions ===

Diels Alder Reactions are [4+2] cycloaddition between a diene and dienophile (usually an alkene with electron-donating or electron-withdrawing groups). The exercises included below are all examples of Diels-Alder reactions. These reactions are usually kinetic and controlled by orbital symmetry.

Diels-Alder reactions can be divided into three different categories according to the relative energies of the reactant orbitals - normal electron demand, neutral electron demand an inverse electron demand. An illustration of the relative orbital energies involved is afforded below (Table 1):

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1: Diels-Alder Electron Demand. EWG - Electron Withdrawing Group; EDG - Electron Donating Group
|-
! style="text-align: center; background: #FFFFFF" | [[File:Sl8514_diels_alder_normal_ed.png|300px]] EWG on dienophile EDG on diene
! style="text-align: center; background: #FFFFFF" | [[File:Sl8514_diels_alder_neutral_ed.png|300px]] Similar substituents on both
! style="text-align: center; background: #FFFFFF" | [[File:Sl8514_diels_alder_inverse_ed.png|300px]] EDG on dienophile EWG on diene
|}

Normal Electron Demand Diels-Alder reactions are characterised by favourable HOMOdiene-LUMOdienophile interactions and the opposite is true for Inverse Electron Demand reactions (HOMOdienophile-LUMOdiene). Normal Electron Demand Diels-Alder reactions are normally faster than Neutral Electron Demand Diels-Alder reactions, which have larger gaps between the diene and dienophile orbitals. As Diels-Alder reactions are usually orbital-controlled, favourable orbital overlaps are very good predictors of more facile reactions.

=== Computational Aims ===

This computational experiment aims to model three different Diels-Alder reactions - butadiene/ethylene (Exercise 1); 1,3-dioxole/cyclohexadiene (Exercise 2) and SO2-1,2-dimethylenebenzene (Exercise 3). In addition, an alternative cheletropic pathway in the SO2-1,2-dimethylenebenzene reaction is explored and compared with the Diels-Alder reactions.

== Methods and Basis Sets used ==

For all three exercises, product structures were first optimised to minima. Afterwards, bonds formed during the reaction were removed and fragments were edited to resemble reactants. These were moved apart and the structure was frozen into a "Guess Transition State" and optimised to a minima, followed by optimisation to a transition state after removal of redundant coordinates. Intrinsic Reaction Coordinate (IRC) calculations were then performed to visualise the entire reaction path.

Calculations in Exercise 1 and 3 were performed with the semi-empirical PM6 method, which offers a reasonable amount of accuracy and a much faster computational time. Calculations in Exercise 2 was first performed with PM6, and then further optimised with the ''ab initio'' DFT method with the B3LYP/6-31G(d) basis set. All transition state calculations were performed with the ''noeigen'' keyword and the ultrafine grid. In all non-transition state structures, good convergence was observed and no imaginary frequencies were found. In all transition-state structures, good convergence was observed and one imaginary frequency corresponding to the predicted reaction trajectory was found.

== Exercise 1: Reaction between Butadiene and Ethylene ==

[[File:Sl8514_ex1_reaction_scheme.jpg|750px|thumb|center|Fig. 1: Ex 1 Reaction Scheme with mechanism]]

The reaction documented above is the simplest possible Diels-Alder reaction. This reaction is modeled with the semi-empirical PM6 method.
 
=== MO analysis and Orbital Symmetries ===

Frontier Molecular Orbitals (FMOs) of the reactants and transition state are visualised below. The table on the left shows screenshots of the FMOs from GaussView, and the diagram on the right traces the FMO overlaps with ChemDraw.

 [[File:Sl8514_ex1_MO_diagram_redo.png|450px|thumb|right|Fig. 2: Ex 1 MO diagram of frontier orbitals]]

{| class="wikitable"
|+ Summary of Calculated MOs (Exercise 1, Table 1)
! style="background: #0D4F8B; color: white;" | Species
! colspan="2" style="background: #0D4F8B; color: white;" | MO
! colspan="2" style="background: #0D4F8B; color: white;" | MO
|-
! style="background: #0D4F8B; color: white;" | Butadiene
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_scis_butadiene_homo.PNG]] HOMO Antisymmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_scis_butadiene_lumo.PNG]] LUMO Symmetric
|-
! style="background: #0D4F8B; color: white;" | Ethylene
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ethylene_lumo.PNG]] LUMO Antisymmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ethylene_homo.PNG]] HOMO Symmetric
|-
! style="background: #0D4F8B; color: white;" | Transition State
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex1_homo-1.PNG]] HOMO-1 Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex1_lumo+1.PNG]] LUMO Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_cyclohexene_ts_homo.PNG]] HOMO Symmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_cyclohexene_ts_lumo.PNG]] LUMO+1 Symmetric
|}

 The reaction proceeds via a 6π electron electrocyclic reaction.

As seen on the MO diagram on the right (Fig. 2), reactions are only symmetry-allowed when the reactant orbital symmetries are identical. For example, the antisymmetric HOMO of butadiene reacts with the antisymmetric LUMO of ethylene even though the symmetric ethylene HOMO is much closer in energy. This can be explained by the orbital overlap integral. If symmetric and antisymmetric orbitals interact, the orbital overlap will be zero. Therefore, new molecular orbitals cannot be formed and the molecules do not react in that particular manner.

Resultant MO bonding-antibonding pairs will carry the same symmetry label as their constituent MOs. This can be seen by how the pairs (HOMO-1,LUMO) and (HOMO, LUMO+1) retained the same symmetry labels as their constituent MOs in the table above.

=== Bond Distances ===

Changes in bond distances are documented below:

[[File:Sl8514_ex1_numbered_cyclohexene.png|150px|thumb|right|Fig. 3: Numbered Cyclohexene]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Summary of Carbon Internuclear Distances / Å (Exercise 1, Table 2)
! style="background: #0D4F8B; color: white;" | Species
! style="background: #0D4F8B; color: white;" | C1-C2
! style="background: #0D4F8B; color: white;" | C2-C3
! style="background: #0D4F8B; color: white;" | C3-C4
! style="background: #0D4F8B; color: white;" | C4-C5
! style="background: #0D4F8B; color: white;" | C5-C6
! style="background: #0D4F8B; color: white;" | C6-C1
|-
! style="background: #0D4F8B; color: white;" | Butadiene
! style="text-align: center" | 1.47079
! style="text-align: center" | 1.33343
! style="text-align: center" | -
! style="text-align: center" | -
! style="text-align: center" | -
! style="text-align: center" | 1.33342
|-
! style="background: #0D4F8B; color: white;" | Ethylene
! style="text-align: center" | -
! style="text-align: center" | -
! style="text-align: center" | -
! style="text-align: center" | 1.32731
! style="text-align: center" | -
! style="text-align: center" | -
|-
! style="background: #0D4F8B; color: white;" | Transition State
! style="text-align: center" | 1.41111
! style="text-align: center" | 1.37973
! style="text-align: center" | 2.11507
! style="text-align: center" | 1.38174
! style="text-align: center" | 2.11435
! style="text-align: center" | 1.37978
|-
! style="background: #0D4F8B; color: white;" | Product
! style="text-align: center" | 1.33700
! style="text-align: center" | 1.50087
! style="text-align: center" | 1.53711
! style="text-align: center" | 1.53456
! style="text-align: center" | 1.53709
! style="text-align: center" | 1.50086
|}

 
The van der Waals radius of carbon is 1.70 Å, and the typical length of a sp3-sp3 C-C bond is 1.53 Å and the typical length of a sp2-sp2 C=C bond is 1.34 Å.<ref name="CC bond lengths" />

Distance between C4 and C5 increases in both the transition state and the final product due to the C=C double bond (sp2) in ethylene changing to a C-C single bond (sp3). Likewise, bond lengths between C1 and C6 and C2 and C3 lengthen as the C=C double bonds change to C-C single bonds. Bond lengths between C1 and C2 shorten as the C=C double bond is formed via a partial double bond in the transition state. The developing bonds between C3-C4 and C5-C6 in the transition state have the longest bond lengths in the table. However, these are still shorter than the twice the van der Waals radii of two carbon atoms (3.40 Å), implying that bonding interactions are present.

In the product, the C2-C3 and C6-C1 bond lengths are both slightly shorter than the typical sp3-sp3 C-C bond lengths. This suggests a small degree of additional hyperconjugation between neighbouring C-H σ bonds and the C=C π bond, resulting in a small contraction in the bonds.
 
[[File:Sl8514 ex1 bond dist plot.PNG|center]]
 

The graph above characterises the C-C bond length variations throughout the reaction.

The approach of the dienophile is shown by steadily decreasing C3-C4 bond lengths and C5-C6 bond lengths (both graphs overlap exactly). At the reaction coordinate shown by the black dotted line, the transition state is reached. The transition state is characterised by identical C1-C6, C1-C2, C2-C3 and C4-C5 bond lengths due to delocalisation, and longer C3-C4 distances. Eventually, the C1-C2 bond length, C3-C4 and C5-C6 bond lengths contract to form a sp2 C=C bond and two sp3 C-C bond lengths respectively. C2-C3, C1-C6 and C4-C5 bonds lengthen to form three sp3 bonds.

=== Vibrations and Reaction Path ===

An Intrinsic Reaction Coordinate (IRC) calculation was performed on the obtained transition state. The vibration corresponding to the imaginary frequency in the transition state and the reaction path obtained from the IRC calculation are animated below:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Vibrations and Reaction Path (Exercise 1, Table 3)
! style="background: #0D4F8B; color: white;" | Vibration
! style="background: #0D4F8B; color: white;" | Reaction Path
|-
! style="background: #8080CC;" | [[File:Sl8514_ex1_imaginfreq_cropped.gif]] 948.8 i cm-1
! style="background: #8080CC;" | [[File:Sl8514_ex1_reactionpath_reverse_cropped.gif]]
|}

The imaginary mode is a good reflection of the eventual path of the reaction.

This Diels-Alder reaction is '''''synchronous''''', meaning that bond formation on each side of the reactant occurs simultaneously and at the same rate.

== Exercise 2: Reaction between 1,3-dioxole and 1,3-cyclohexadiene ==

[[File:Sl8514_ex2_reaction_scheme.png|500px|thumb|center|Fig. 4: Reaction Scheme of reaction between 1,3-dioxole and 1,3-cyclohexadiene]]
 

1,3-Dioxole can react with cyclohexadiene to form exo and endo adducts in two [4+2] Diels-Alder cycloaddition pathways. This reaction was simulated with the B3LYP/6-31G(d) basis set and the DFT method, following methodologies stated in the [[Methods and Basis Sets]] section. Unlike Exercise 1, this reaction contains two oxygen atoms on the dienophile (1,3-Dioxole), which may interfere with the orbital energies, producing better overlap as examined below.

=== MO Analysis ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Summary of Calculated MOs for Exo and Endo TS (Exercise 2, Table 4)
! style="background: #0D4F8B; color: white;" | Species
! colspan="2" style="background: #0D4F8B; color: white;" | MO
! colspan="2" style="background: #0D4F8B; color: white;" | Chemdraw Representation
! colspan="2" style="background: #0D4F8B; color: white;" | MO
! colspan="2" style="background: #0D4F8B; color: white;" | Chemdraw Representation
|-
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole
! colspan="2" style="background: #FFFFFF; text-align: center;" | [[File:Sl8514_13dioxole_homo.PNG|120px]] HOMO Symmetric
! colspan="2" style="background: #FFFFFF; text-align: center;" | [[File:Sl8514_13dioxole_homo_chemdraw.png|100px]] HOMO Symmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_13dioxole_lumo.PNG|120px]] LUMO Antisymmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_13dioxole_lumo_chemdraw.png|100px]] LUMO Antisymmetric
|-
! style="background: #0D4F8B; color: white;" | Cyclobutadiene
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_cyclohexadiene_lumo.PNG|120px]] LUMO Symmetric
! colspan="2" style="background: #FFFFFF; text-align: center;" | [[File:Sl8514_cyclohexadiene_lumo_chemdraw.png|100px]] LUMO Symmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_cyclohexadiene_homo.PNG|120px]] HOMO Antisymmetric
! colspan="2" style="background: #FFFFFF; text-align: center" | [[File:Sl8514_cyclohexadiene_homo_chemdraw.png|100px]] HOMO Antisymmetric
|-
! style="background: #0D4F8B; color: white;" | Transition State Exo
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_EX2_EXO_TS_B3LYP_6-31GD_GFPRINT.LOG</uploadedFileContents>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Symmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_EX2_EXO_TS_B3LYP_6-31GD_GFPRINT.LOG</uploadedFileContents>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Symmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_exo_homo-1_chemdraw.png|120px]] HOMO Symmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_exo_lumo+1_chemdraw.png|120px]] LUMO Symmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_EX2_EXO_TS_B3LYP_6-31GD_GFPRINT.LOG</uploadedFileContents>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Antisymmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_EX2_EXO_TS_B3LYP_6-31GD_GFPRINT.LOG</uploadedFileContents>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_exo_homo_chemdraw.png|120px]] HOMO-1 Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_exo_lumo_chemdraw.png|120px]] LUMO+1 Antisymmetric
|-
! style="background: #0D4F8B; color: white;" | Transition State Endo
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>HOMO</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514 ex2 endo ts b3lyp 631gd gfprint.log</uploadedFileContents>
<script>frame 28; mo 41; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Symmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>LUMO</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_ex2_endo_ts_b3lyp_631gd_gfprint.log</uploadedFileContents>
<script>frame 28; mo 42; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Symmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_endo_homo-1_chemdraw.png|120px]] HOMO Symmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_endo_lumo_chemdraw.png|120px]] LUMO Symmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>HOMO-1</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_ex2_endo_ts_b3lyp_631gd_gfprint.log</uploadedFileContents>
<script>frame 28; mo 40; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Antisymmetric
! style="background: #FFFFFF; text-align: center" | <jmol><jmolApplet>
<title>LUMO+1</title>
<color>white</color>
<size>150</size>
<uploadedFileContents>Sl8514_ex2_endo_ts_b3lyp_631gd_gfprint.log</uploadedFileContents>
<script>frame 28; mo 43; mo nodots nomesh fill translucent; mo titleformat "";mo cutoff 0.01; rotate z -90 </script>
</jmolApplet></jmol>Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_endo_homo_chemdraw.png|120px]] HOMO-1 Antisymmetric
! style="background: #FFFFFF; text-align: center" | [[File:Sl8514_ex2_endo_lumo+1_chemdraw.png|120px]] LUMO+1 Antisymmetric
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ MO Diagrams (Exercise 2, Table 4)
! style="background: #0D4F8B; color: white;" | Exo TS
! style="background: #0D4F8B; color: white;" | Endo TS
|-
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_exo_mo_diagram_redo.png|400px]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_endo_mo_diagram_redo.png|400px]]
|}

In a similar fashion as Exercise 1, only orbitals of identical symmetry combine to produce new orbitals in the transition state, as illustrated in both the table and the Chemdraw diagrams. Contrary to Exercise 1, the energy levels of the dienophile (1,3-dioxole) is shifted higher. This is due to the presence of two π-electron donating oxygen atoms adjacent to the alkene, causing the electron density of the alkene to increase and hence pushing the orbitals higher in energy. Therefore, the symmetric HOMO of the dienophile and symmetric LUMO of the diene are much closer in energy compared to Exercise 1, resulting in stronger mixing and a larger stabilisation energy. The stronger orbital interactions will result in a faster and more favourable reaction compared to Exercise 1, although direct comparison of energies are not possible here as the calculations were done in different basis sets. This also identifies the Diels-Alder reaction between 1,3-dioxole and cyclohexadiene as an '''''inverse electron demand''''' Diels-Alder reaction.

=== Vibration and Reaction Path ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Vibrations and Reaction Path (Exercise 1, Table 3)
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | Vibration
! style="background: #0D4F8B; color: white;" | Reaction Path
|-
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #8080CC;" | [[File:Sl8514_ex2_exo_vibration_2_crop.gif]] 528.8 i cm-1
! style="background: #8080CC;" | [[File:Sl8514_ex2_exo_irc_2_revcropped.gif]]
|-
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #8080CC;" | [[File:Sl8514_ex2_endo_ts_vibration_2_crop.gif]] 520.9 i cm-1
! style="background: #8080CC;" | [[File:Sl8514_ex2_endo_irc_2_revcropped.gif]]
|}

As in Exercise 1, the imaginary frequency present in the transition state closely follows the reaction trajectory.

In both reaction pathways, both molecules approach each other in planar configurations and the sp3 C-C single bond rotates to its higher-energy eclipsed conformer. The rotation will prevent steric interactions between hydrogen atoms on the cyclohexene ring and the approaching dioxole. Both carbons are then locked in the eclipsed conformation in the product due to the new bridge on the cyclohexene ring.

=== Reaction Path Energies (Thermochemistry) ===

Free energies of all products, reactants and transition states taken from the .log files of the calculations are presented below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Summary of Sum of Electronic and Thermal Free Energies
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | 1,3-Dioxole / Eh
! style="background: #0D4F8B; color: white;" | Cyclohexadiene / Eh
! style="background: #0D4F8B; color: white;" | TS / Eh
! style="background: #0D4F8B; color: white;" | Product / Eh
! style="background: #0D4F8B; color: white;" | Reaction Barrier / kJmol-1
! style="background: #0D4F8B; color: white;" | Reaction Energy / kJmol-1
|-
! style="background: #0D4F8B; color: white;" | Exo
! rowspan="2" style="background: #FFFFFF; text-align: center" | -267.068642
! rowspan="2" style="background: #FFFFFF; text-align: center" | -233.324375
! style="background: #FFFFFF; text-align: center" | -500.329165
! style="background: #FFFFFF; text-align: center" | -500.373258
! style="background: #FFFFFF; text-align: center" | 167.6
! style="background: #FFFFFF; text-align: center" | -64.1
|-
! style="background: #0D4F8B; color: white;" | Endo
! style="background: #FFFFFF; text-align: center" | -500.332153
! style="background: #FFFFFF; text-align: center" | -500.418691
! style="background: #FFFFFF; text-align: center" | 159.8
! style="background: #FFFFFF; text-align: center" | -67.4
|}

[[File:Sl8514_ex2_reaction_energy.png|450px|center]]

As the endo pathway has a lower reaction barrier and a lower reaction energy, it is both the kinetic and thermodynamic product. Therefore, it is likely to be produced in significant excess in a reaction under kinetic or thermodynamic conditions.

=== Secondary Orbital Interactions and Sterics===

The Endo pathway has a smaller activation barrier as the transition state is more stable (of lower energy) compared to that of the Exo pathway. This is because the transition state is stabilised by secondary orbital interactions, which are illustrated in the table below:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Secondary Orbital Interactions
! style="background: #0D4F8B; color: white;" | HOMO
! style="background: #0D4F8B; color: white;" | ChemDraw of HOMO
! style="background: #0D4F8B; color: white;" | LUMO+1
! style="background: #0D4F8B; color: white;" | ChemDraw of LUMO+1
|-
! style="background: #FFFFFF;" | [[File:Sl8514_endots_homo2_-_Copy.PNG]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_endo_homo_interactions.png|200px]]
! style="background: #FFFFFF;" | [[File:Sl8514_endots_lumo2_-_Copy.PNG]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_endo_lumo+1_interactions.png|200px]]
|}

In the endo transition state structure, the p orbitals on oxygen in 1,3-dioxole are of the correct symmetry and are large enough to overlap with alkene p-orbitals in cyclohexadiene. This produces stabilising interactions in TS orbitals HOMO and LUMO+1, resulting in a lower energy transition state and hence a lower activation energy.

The Exo product has a higher energy compared the Endo product due to destabilising steric interactions, as shown below:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Steric Repulsion in Exo and Endo products
! style="background: #0D4F8B; color: white;" | Exo
! style="background: #0D4F8B; color: white;" | Endo
|-
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_exo_product.PNG|350px]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex2_endo_pdt_steric.png|250px]]
|}

As shown in the table above, hydrogens in the carbon of the 1,3-dioxole ring will clash with hydrogens on the carbon bridge, resulting in destabilising interactions. This results in the exo structure being higher in energy than the endo structure, which does not suffer from such steric clashes.

== Exercise 3 ==

[[File:Sl8514_ex3_reaction_scheme.png|400px|center]]

Sulfur dioxide can react with 1,2-dimethylenebenzene via two diels-alder pathways (exo and endo) and a cheletropic pathway as shown above. This exercise investigates the energies of all three different pathways and visualises the reaction paths with Intrinsic Reaction Coordinate calculations.

All calculations were performed with the semi-empirical PM6 method.

=== Illustrations of IRCs ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Pathways
! style="background: #0D4F8B; color: white;" | Diels Alder Exo
! style="background: #0D4F8B; color: white;" | Diels Alder Endo
! style="background: #0D4F8B; color: white;" | Cheletropic

|-
! style="background: #8080CC; text-align: center" | [[File:Sl8514_ex3_DA_irc_revcropped.gif]]
! style="background: #8080CC; text-align: center" | [[File:Sl8514_ex3_DA_endo_irc_cropped.gif]]
! style="background: #8080CC; text-align: center" | [[File:Sl8514_ex3_cheletropic_irc_cropped.gif]]
|-
! style="background: #FFFFFF;" | [[File:Sl8514_ex3_DA_irc_graph.PNG|300px]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex3_DA_endo_irc_graph.PNG|300px]]
! style="background: #FFFFFF;" | [[File:Sl8514_ex3_cheletropic_irc_graph.PNG|300px]]
|}

Both Diels-Alder pathways feature asynchronous bond formation, as the C-O bond is formed before the C-S bond. As oxygen is more electronegative than sulfur, it will have a larger δ- compared to sulfur, causing bond formation to be asynchronous due to differences in electron density. However, bond formation in the cheletropic pathway is synchronous as there is no disparity in the dipole moments.

=== Pathway Energies ===

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Summary of Sum of Electronic and Thermal Free Energies
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | SO2 / Eh
! style="background: #0D4F8B; color: white;" | 1,2-dimethylenebenzene / Eh
! style="background: #0D4F8B; color: white;" | TS / Eh
! style="background: #0D4F8B; color: white;" | Product / Eh
! style="background: #0D4F8B; color: white;" | Reaction Barrier / kJmol-1
! style="background: #0D4F8B; color: white;" | Reaction Energy / kJmol-1
|-
! style="background: #0D4F8B; color: white;" | Exo
! rowspan="3" style="text-align: center" | -0.118614
! rowspan="3" style="text-align: center" | 0.178
! style="text-align: center" | 0.092075
! style="text-align: center" | 0.021451
! style="text-align: center" | 85.8
! style="text-align: center" | -99.6
|-
! style="background: #0D4F8B; color: white;" | Endo
! style="text-align: center" | 0.090559
! style="text-align: center" | 0.021698
! style="text-align: center" | 81.8
! style="text-align: center" | -98.9
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
! style="text-align: center" | 0.095059
! style="text-align: center" | 0.000005
! style="text-align: center" | 93.7
! style="text-align: center" | -155.9
|}

[[File:Sl8514_ex3_pathways.png|400px|center]]

Under kinetic conditions, the endo product would be formed preferentially as it has the lowest energy transition state. Under thermodynamic/equilibrating conditions, however, the cheletropic product will be formed preferentially as it is the lowest energy product.

Xylylene is inherently unstable<ref name="Xylylene" />; once the Diels-Alder adduct is formed it undergoes rapid fragmentation into the reactants. Cheletropic products, however, were much more stable than the Diels-Alder products. This is in agreement with the calculations performed.

== Conclusion ==

Three Diels-Alder reaction (butadiene/ethylene in Exercise 1; 1,3-dioxole/cyclohexadiene in Exercise 2; SO2/1,2-dimethylenebenzene in Exercise 3) have been examined with the semi-empirical PM6 method and ''ab initio'' DFT method with the B3LYP/6-31G(d) basis set. An additional cheletropic pathway has been examined in '''Exercise 3'''. All reactants and products have been optimised to minima and all transition states have been optimised to first-order saddle points. All three reaction paths have been fully visualised with IRC calculations. Molecular orbitals in the transition state and reactants have also been visualised. Upon examination of the Frontier Molecular Orbitals (FMOs), the electron demand of the Diels-Alder reaction in '''Exercise 2''' has been determined as an inverse electron demand Diels-Alder reaction. Energies of ''Exo'' and ''Endo'' pathways in '''Exercise 2''' and '''Exercise 3''' have been compared. In '''Exercise 2''', the Endo pathway was deemed to be the most stable kinetically and thermodynamically. In '''Exercise 3''', the endo product is deemed as the kinetic product while the cheletropic product is the most thermodynamically stable product despite it having the highest reaction barrier.

== References ==
<references>
<ref name="CC bond lengths">D. R. Lide, Tetrahedron, 1962, 17, 125–134.</ref>
<ref name="Xylylene">D. Suarez, T. L. Sordo, J. A. Sordo, J. Org. Chem., 1995, 60 (9), 2848–2852</ref>
</references>

== Log files of calculations ==

 '''Exercise 1'''
 [[File:SL8514_CYCLOHEXENE_PM6.LOG]]
 [[File:SL8514_CYCLOHEXENE_TS_PM6.LOG]]
 [[File:SL8514_ETHYLENE_PM6.LOG]]
 [[File:SL8514_SCIS_BUTADIENE_PM6.LOG]]
 [[File:SL8514_CYCLOHEXENE_IRC_PM6.LOG]]
 [[File:SL8514_CYCLOHEXENE_PRE_TS_MODRED_PM6.LOG]]
 
 '''Exercise 2'''

File:SL8514 CYCLOHEXENE PRE TS MODRED PM6.LOG

2017-03-09T18:51:02Z

Sl8514:

File:SL8514 CYCLOHEXENE IRC PM6.LOG

2017-03-09T18:49:16Z

Sl8514: