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Rep:Mod:wcc14geeTS

2018-02-14T03:41:39Z

Wcc14: /* Conclusion */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|text-below|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
|
|
|
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}
|
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition states and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to the cheletropic reaction as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) is forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. The driving force for these reactions is the formation of the aromatic benzene ring, stabilising the reactions to become more thermodynamically favourable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic and thermodynamically and kinetically unfavourable.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:40:30Z

Wcc14: /* Conclusion */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|text-below|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
|
|
|
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}
|
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition states and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to the cheletropic reaction as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) is forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. The driving force for these reactions is the formation of benzene ring to gain stability. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:35:20Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|text-below|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
|
|
|
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}
|
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition states and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to the cheletropic reaction as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:29:26Z

Wcc14: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|text-below|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
|
|
|
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}
|
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition states and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:27:27Z

Wcc14: /* Bond Length Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|text-below|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
|
|
|
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}
|
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:22:37Z

Wcc14: /* Molecular Orbital Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-antisymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:22:09Z

Wcc14: /* Molecular Orbital Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interact with each other, meaning symmetric-symmetric interaction and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:20:40Z

Wcc14: /* Exercise 1: Reaction of Butadiene with Ethylene */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|400px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:17:03Z

Wcc14: /* References */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">Secondary Orbital Interaction, http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf, (accessed Feb 2018)</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:15:29Z

Wcc14: /* Instability of o-Xylylene */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule<ref name="Huckel" /> (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:15:12Z

Wcc14: /* Instability of o-Xylylene */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons)<ref name="Huckel" /> so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:14:27Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7).<ref name="SOI" /> Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:13:02Z

Wcc14: /* Molecular Orbital Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.<ref name="IDA1" /> <ref name="IDA2" />

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:12:27Z

Wcc14: /* Vibration Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel.<ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:12:13Z

Wcc14: /* Vibration Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. <ref name="Concerted" />
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:11:44Z

Wcc14: /* Bond Length Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54 <ref name=" C length" />
| 1.33 <ref name=" C length" />
| 1.77 <ref name=" VDW" />
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:10:57Z

Wcc14: /* Bond Length Analysis */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3 <ref name=" C length" />
! style="background: #0D4F8B; color: white;" | Csp2-Csp2 <ref name=" C length" />
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom <ref name=" VDW" />
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:09:45Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry.<ref name="PES" /> When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T03:08:54Z

Wcc14: /* References */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

<references>
<ref name="PES">Potential Energy Surface, http://vergil.chemistry.gatech.edu/courses/chem6485/pdf/pes-lecture.pdf, (accessed Feb 2018)</ref>
<ref name="C length">A. G. Orpen, L. Brammer, F. H. Allen, O. Kennard, D. G. Watson and R. Taylor, J. Chem. Soc. Dalt. Trans., 1987, S1–S83.</ref>
<ref name="VDW">A. Bondi, J. Phys. Chem., 1964, 68, 441–451.</ref>
<ref name="Concerted">M. J. S. Dewar, J. J. P. Stewart and S. Olivella, J. Am. Chem. Soc., 1986, 108, 5771–5779.</ref>
<ref name="IDA1">P. Rooshenas, K. Hof, P. R. Schreiner and C. M. Williams, European J. Org. Chem., 2011, 2011, 983–992.</ref>
<ref name="IDA2">A. T. Dang, D. O. Miller, L. N. Dawe and G. J. Bodwell, Org. Lett., 2008, 10, 233–236.</ref>
<ref name="SOI">P. V. Alston, R. M. Ottenbrite and T. Cohen, J. Org. Chem., 1978, 43, 1864–1867.</ref>
<ref name="Huckel">W. E. von Doering and F. L. Detert, J. Am. Chem. Soc., 1951, 73, 876–877.</ref>
</references>

Rep:Mod:wcc14geeTS

2018-02-14T02:52:16Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/6-31G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T02:52:00Z

Wcc14: /* Conclusion */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/631G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with the semi-empirical PM6 or DFT-B3LYP/6-31G(d) methods. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T02:50:32Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/631G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive and energy increases in both directions from this point. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T02:47:28Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/631G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive, energy increases in both directions. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T02:45:41Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/631G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. A potential energy surface is a mathematical function that gives the relationship between the energy of the molecule and its geometry with. When all the vibrational frequencies are real, the structure is a minimum. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive, energy increases in both directions. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative, energy decreases from this point. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T02:33:40Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, three different pericyclic reactions are studied. They are Diels-Alder reaction (exercise 1), inverse electron demand Diels-Alder reaction (exercise 2) and Hetero Diels-Alder reaction (3). Diels-Alder reaction usually undergoes two pathways, endo and exo. However, competing pathway can exist like cheletropic. All these pathways can be analysed by the computational method in order to understand their rate and product stability.

: Gaussian is used to do all the calculations, the semi-empirical PM6 and DFT-B3LYP/631G(d) electronic structure methods are mainly used. The reactants and products of all reactions are optimised to the minimum and also all the transition states. PM6 is used to generate initial geometries while DFT-B3LYP gives a more detailed and accurate optimisation. This is because a higher number of the basis set is involved in the DFT-B3LYP calculation. A basis set is a set of functions that resemble the atomic orbitals (building block of molecular orbitals) and molecular orbitals are generated when basis sets combine linearly.

: Molecular vibrations are shown by performing frequency calculations, which can be used to confirm the position on the potential energy surface. When all the vibrational frequencies are real, the structure is a minima. The minima give the equilibrium position of the molecules, where the gradient is zero and the second derivative is positive. Minima usually correspond to the reactants and products. The minimum energy pathway between two minima is represented by the intrinsic reaction coordinate. When one imaginary vibrational frequency presence, the structure is at its transition state. The transition state is at the maximum of the minimum energy pathway with zero gradient and negative second derivative. IRC calculations are calculated by force constants in order to predict the reaction path after transition state.

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T01:25:05Z

Wcc14: /* Introduction */

'''Transition States and Reactivity'''

= Introduction =

: In this computational lab, 3 different pe

= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS Ex1 Jmol TS

2018-02-14T01:02:26Z

Wcc14: /* JMol Objects for The Transition State of Butadiene and Ethylene Reaction */

=== JMol Objects for The Transition State of Butadiene and Ethylene Reaction ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
! colspan="2" style="background: #0D4F8B; color: white;" | Antisymmetric-Antisymmetric Interaction
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE WITH ETHYLENETS PM6 wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE WITH ETHYLENETS PM6 wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! 2π
! 5π*
|-
! colspan="6" style="background: #0D4F8B; color: white;" | Symmetric-Symmetric Interaction
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE WITH ETHYLENETS PM6 wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE WITH ETHYLENETS PM6 wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! 3π
! 4π*
|}

Rep:Mod:wcc14geeTS Ex1 Jmol Reactants

2018-02-14T01:01:29Z

Wcc14: /* JMol Objects for HOMO And LUMO of Butadiene and Ethylene */

=== JMol Objects for HOMO And LUMO of Butadiene and Ethylene ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Butadiene
! style="background: #0D4F8B; color: white;" | Ethylene
|-
! style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE (OPTIMISE TO MINIMUM) WCC14GEE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_(OPTIMISE_TO_MINIMUM)_wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>BUTADIENE (OPTIMISE TO MINIMUM) WCC14GEE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE_(OPTIMISE_TO_MINIMUM)_wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Rep:Mod:wcc14geeTS Ex2 Jmol TS

2018-02-14T01:01:04Z

Wcc14: /* JMol Objects for Endo Transition State and Exo Transition State */

=== JMol Objects for Endo Transition State and Exo Transition State ===

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Endo Transition State
! style="background: #0D4F8B; color: white;" | Exo Transition State
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | LUMO+1
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="2" | 5π* (antisymmetric)
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | LUMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="2" | 4π* (symmetric)
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | HOMO
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="2" | 3π (symmetric)
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | HOMO-1
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ENDO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 2; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>EXO TS B3LYP wcc14gee.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
! colspan="2" | 2π (antisymmetric)
|}

Rep:Mod:wcc14geeTS

2018-02-14T00:34:17Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T00:33:32Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! style="background: #0D4F8B; color: white;" | Endo
| [[File:OS endo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS endo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! style="background: #0D4F8B; color: white;" | Exo
| [[File:OS exo IRC movie wcc14gee.gif|centre|500px]]
| [[File:OS exo IRC energy path wcc14gee.PNG|centre|500px]]
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-14T00:30:08Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: IRC calculations are shown below.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: IRC Calculations and Total Energy along IRC for Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene and SO2
|-
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! style="background: #0D4F8B; color: white;" | Endo
|
|
|-
! style="background: #0D4F8B; color: white;" | Exo
|
|
|}

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-13T20:20:44Z

Wcc14: /* Conclusion */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This is an inverse electron demand Diels-Alder reaction meaning the LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals and interact the strongest. The calculated activation energy shows that the endo pathway is more kinetically favourable because of secondary orbital interaction between the oxygens and the p-orbital of cyclohexadiene. Since steric hindrance is present in the exo product, therefore raises its energy leading the endo product being thermodynamic. Thus, the endo pathway in this reaction is both kinetically and thermodynamically favourable.

: The reaction between o-xylylene and sulphur dioxide is the final reaction. This reaction can undergo via Diels-Alder or cheletropic. Similar to the reaction in exercise 2, if this reaction proceeds via Diels-Alder, it can form both endo and exo products. Once again, the endo pathway has the lowest activation energy hence most kinetically favourable. The cheletropic product is the thermodynamically favourable product because it is the most stable. When sulphur dioxide reacts with the internal butadiene fragment of o-xylylene, both endo and exo Diels-Alder reactions are endothermic.

= References =

Rep:Mod:wcc14geeTS

2018-02-13T19:59:37Z

Wcc14: /* Conclusion */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

: Three different pericyclic reactions are studied in this computational lab. The reactants, transition states and products of these reactions are optimised with Gaussian. Through Gaussian calculation, energies, vibrational frequencies and intrinsic reaction coordinates for all the molecules are obtained.

: In exercise 1, a [4+2] cycloaddition reaction between butadiene and ethylene is studied. It can be concluded that in order for molecular orbitals to interact, they have to have the same symmetry (symmetric and symmetric interaction or antisymmetric and antisymmetric interaction). Reactions with different symmetry (symmetric and antisymmetric interaction) are forbidden. The negative vibrational frequency of the transition state and IRC proved that this reaction proceeds via a concerted mechanism meaning the formation of new bonds are synchronous.

: Another Diels-Alder reaction is studied in exercise 2. The reaction between cyclohexadiene and 1,3-dioxole can proceed via two pathways, endo and exo. This reaction is an inverse

In the reaction of cyclohexadiene and 1,3-dioxole, both the endo and exo transition states were investigated. In general, the endo transition state is kinetically more favourable as it has lower activation barrier, possibly due to the secondary orbital interaction between the lone pair in p orbital on the oxygen atom and the empty π* orbital in the diene, which stabilises the transition state. However, the exo transition state is thermodynamically favourable due to less steric hindrance, hence if sufficient energy is supplied to the system, formation of the exo product could be possible.

The final reaction between xylylene and SO2 again proved that the endo Diels-Alder transition state has the lowest activation energy, making it kinetically favourable at low temperature. However, the cheletropic product is the most stabilised and thermodynamically favourable product. Therefore the reaction would yield the cheletropic product under thermodynamic control instead of the exo Diels-Alder product.

= References =

Rep:Mod:wcc14geeTS

2018-02-13T19:11:12Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathways
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png

2018-02-13T19:09:36Z

Wcc14: Wcc14 uploaded a new version of File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png

Rep:Mod:wcc14geeTS

2018-02-13T19:06:31Z

Wcc14: /* Instability of o-Xylylene */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|texxt-bottom|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T19:02:57Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and p-orbitals of cyclohexadiene (Figure 7). Secondary orbital interaction is not expected in the exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
| [[File:Secondary orbital interaction wcc14gee.PNG |400px|centre|thumb|Figure 7: Secondary Orbital Interaction between Oxygens And p-Orbitals Showed in Dash Line]]
| [[File:Steric clash wcc14gee.png|400px|right|thumb|Figure 8: Endo Product Showing Steric Clash And Exo Product]]
|}

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product (Figure 8). The steric clash in the exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

File:Secondary orbital interaction wcc14gee.PNG

2018-02-13T18:58:29Z

Wcc14:

Rep:Mod:wcc14geeTS

2018-02-13T18:44:03Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png |400px|centre|thumb|Figure 13: Reaction Profile for Diels-Alder Reaction between External and Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

File:Reaction profile comparing external and internal butadiene fragment wcc14gee.png

2018-02-13T18:42:16Z

Wcc14:

Rep:Mod:wcc14geeTS

2018-02-13T18:40:52Z

Wcc14: /* Instability of o-Xylylene */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus highly unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 13: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

File:Steric clash wcc14gee.png

2018-02-13T18:39:50Z

Wcc14:

Rep:Mod:wcc14geeTS

2018-02-13T18:16:46Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 13: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: As seen from Figure 13, reactions with internal cyclobutadiene fragments are both kinetically and thermodynamically unfavourable. Also, reactions reacting with the internal butadiene fragment, both endo and exo transition states have higher activation energy compared with previous reactions. The reaction energy suggested that reactions with internal butadiene fragment are endothermic.

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T18:05:18Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 6: Energies of Reactants, Transition States and Products for Diels-Alder and Cheletropic Reactions
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Diels-Alder via Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T18:04:14Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

: A rection profile containing reactions with sulphur dioxide reacting with both external and internal butadiene fragment of o-xylene is conducted.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T18:02:07Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment And Sulphur Dioxide
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 267.98
| 172.26
| 110.06
| 14.34
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T17:55:48Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 7: Energies of Reactants, Transition States and Products for Reaction with Internal Butadiene Fragment
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 275.82
| 176.71
| 117.90
| 18.78
|}

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T17:52:53Z

Wcc14: /* Side Reaction Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

= Conclusion =

= References =

Rep:Mod:wcc14geeTS

2018-02-13T17:52:14Z

Wcc14: /* Activation and Reaction Energies Analysis */

'''Transition States and Reactivity'''

= Introduction =
= Exercise 1: Reaction of Butadiene with Ethylene =

: A typical [4+2] cycloaddition Diels-Alder reaction is studied in this exercise. Reacting butadiene and ethylene forms cyclohexene by a concerted mechanism with a cyclic transition state. The reactants, transition state and product are optimised at semi-empirical PM6 level.

: The reaction scheme is show below.
: [[File:Reaction scheme wcc14gee.png|300px|center|thumb|Figure 1: Reaction Scheme of Butadiene And Ethylene]]

=== Molecular Orbital Analysis ===
: The formation of the transition state is through the corresponding π molecular orbital interactions between the HOMO and LUMO of butadiene and ethylene. This is shown by Figure 2 and all the orbitals are labelled with their symmetry (S=symmetric and AS=antisymmetric). The formation of the transition state can be visualised by the JMol objects of the [[Mod:wcc14geeTS_Ex1_Jmol_Reactants|reactants]] (HOMO and LUMO of butadiene and ethylene) and the [[Mod:wcc14geeTS_Ex1_Jmol_TS|transition state orbitals]] (2π, 3π, 4π* and 5π*).

: [[File:Butadiene with ethylene MO wcc14gee.PNG|400px|700xp|centre|thumb|bottom|Figure 2: Molecular Orbital of The Diels-Alder Reaction between Butadiene and Ethylene]]
:
: The MO theory states that a reaction is allowed when the molecular orbitals with same symmetry interacts with each other, meaning symmetric-symmetric interactions and antisymmetric-antisymmetric interaction. Molecular orbitals with different symmetry cannot interact with each other, therefore symmetric-asymmetric interaction is forbidden. In order to overlap efficiently, the molecular orbitals should be close in energy.
:
: In this reaction, the antisymmetric molecular orbital of butadiene (HOMO) interacts with the antisymmetric molecular orbital of diethylene (LUMO) to give the 2π and 5π* molecular orbitals of the transition state; the symmetric molecular orbital of butadiene (LUMO) interacts with the symmetric molecular orbital of diethylene (HOMO) to give the 3π and 4π* molecular orbitals of the transition state.
:
: The overlap integral is zero in a symmetric-asymmetric interaction while non-zero in symmetric-symmetric and antisymmetric-antisymmetric interactions.

=== Bond Length Analysis ===
: As the reaction progress, the bond length changes. Therefore, the bond lengths between different carbon atoms for reactants, transition state and product are studied. The position of different carbon atoms and the result is shown in Figure 3 and Table 1 respectively.
: [[File:Butadiene with ethylene labelling carbon wcc14gee.PNG|400px|center|thumb|Figure 3: Labeling of The Carbon Atoms in The Reaction between Butadiene and Ethylene]]
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 1: The C-C Bond Lengths of Reactants, Transition State And Product
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | State
! colspan="6" style="background: #0D4F8B; color: white;" | Bond / Å
|-
| 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="text-align: center" |Reactants
| style="text-align: center" |1.33
| style="text-align: center" |N/A
| style="text-align: center" |1.34
| style="text-align: center" |1.47
| style="text-align: center" |1.34
| style="text-align: center" |N/A
|-
! style="text-align: center" |Transition State
| style="text-align: center" |1.38
| style="text-align: center" |2.11
| style="text-align: center" |1.38
| style="text-align: center" |1.41
| style="text-align: center" |1.38
| style="text-align: center" |2.11
|-
! style="text-align: center" |Product
| style="text-align: center" |1.54
| style="text-align: center" |1.54
| style="text-align: center" |1.50
| style="text-align: center" |1.34
| style="text-align: center" |1.50
| style="text-align: center" |1.54
|}

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 2: Literature Values of C-C Bond Lengths And Van der Waals Radius of Carbon Atom
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" | Csp3-Csp3
! style="background: #0D4F8B; color: white;" | Csp2-Csp2
! style="background: #0D4F8B; color: white;" | Van der Waals Radius of C atom
|-
! style="background: #0D4F8B; color: white;" |Bond Length / Å
| 1.54
| 1.33
| 1.77
|}
: As seen from the results, during the reaction the reactants' double bonds ( C1-C2, C3-C4 and C5-C6) increase from 1.33Å to 1.54Å. This means the bonds are changing from Csp2-Csp2 to Csp3-Csp3 as the value matches with the literature (Table 2). On the other hand, C4-C5 decreases from 1.47Å to 1.34Å, indicating the formation of C=C (sp2) at the product. The new bonds formed at C2-C3 and C6-C1 are single bond (sp3) with bond length around 1.54Å.
: At the transition state, the distance between C2-C3 and C6-C1 is 2.11Å. Since the distance is shorter than twice the Van der Waals radii of carbon (3.4Å), therefore a bond is forming between C2-C3 and C6-C1.

=== Vibration Analysis ===

: As mentioned above, this [4+2] cycloaddition reaction undergoes a concerted mechanism. A concerted mechanism means all the bond breaking and forming takes place in parallel. (ref)
:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 3: IRC and Negative Frequency at The Transition State
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Negative Frequency (-948) at The Transition State
|-
| [[File:Exercise 1 IRC wcc14gee.gif|centre|500px]]
| [[File:Exercise 1 TS negative frequency.gif|centre|500px]]
|}
: The IRC and the negative frequency at the transition state proves that this is a concerted reaction since both carbons on the ethylene approach butadiene's carbons at the same time. Therefore, the formation of the two new bonds are synchronous.

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

: In this section, another Diels-Alder reaction is studied. The reaction between cyclohexadiene and 1,3-dioxole can go under two pathways (endo and exo) to form two products. This is shown in the reaction scheme below. The reaction barrier and reaction energy of the two pathways are calculated by Gaussian in order to determine the kinetic and thermodynamically products. All reactants, transition state and products are optimised to DFT B-3LYP/6-31G(d) level.

: [[File:Cyclohexadiene and dioxole reaction scheme wcc14gee.PNG|500px|center|thumb|Figure 4: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

=== Molecular Orbital Analysis ===

: [[File:Cyclohexadiene and dixole MO wcc14gee.png|500px|700xp|center|thumb|Figure 5: Reaction Scheme for The Reaction between Cyclohexadiene and 1,3-Dioxole]]

: The MO diagram for this reaction is shown in Figure 5. As mentioned in exercise 1, only molecular orbitals with same symmetry can interact. From both the Jmol objects of [[Mod:wcc14geeTS_Ex2_Jmol_TS|endo and exo transition state]], it can be seen that both HOMO and LUMO of the transition states are symmetric. Referring to the MO diagram, this means the LUMO of cyclohexadiene interacts with the HOMO of 1,3-dioxole to produce the 3π (HOMO) and 4π* (LUMO) orbitals of the transition states. This is confirmed by calculating the energy of the orbitals for both transition states using single point energy calculation.

: This also suggests an inverse electron demand Diels-Alder reaction, cycloaddition between an electron-rich dienophile and an electron-poor diene. The energy level of the dienophile is raised by the electron donating oxygens in 1,3-dioxole leading to LUMOcyclohexadiene and HOMO1,3-dioxole are closer in energy than the HOMOcyclohexadiene and LUMO1,3-dioxole. Thus LUMOcyclohexadiene and HOMO1,3-dioxole are the frontier orbitals that interact the stongest and hence a shift of MO energy order.

=== Activation and Reaction Energies Analysis ===

: Table 4 shows the energy of reactants, products and transition states calculated by Gaussian. The energy of the reactants is the sum of the energies of cyclohexadiene and 1,3-dioxole, assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is drawn using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| -1313781.87
| -1313622.07
| -1313849.27
| 159.80
| -67.40
|-
! style="background: #0D4F8B; color: white;" | Exo
| -1313781.87
| -1313614.22
| -1313845.68
| 167.65
| -63.81
|}
|
|
|
|
| [[File:2-DA Reaction Energy Diagram wcc14gee.png|400px|centre|thumb|Figure 6: Reaction Profile of Cyclohexadiene and 1,3-Dioxole]]
|}

: In a Diels-Alder reaction, the endo pathway is typically kinetically favourable. This is reflected in the calculated results since the endo pathway has a lower activation energy (Figure 6) and a more stable transition state. This is due to the secondary orbital interaction between the oxygen and back lobes of the cyclohexadiene HOMO. Secondary orbital interaction is not expected in the Exo pathway because the oxygens are pointed away from the cyclohexadiene p-orbitals.

: In a typical Diels-Alder reaction, the Exo product is expected to be more thermodynamically favourable because of less sterically crowded. However, the calculated results show that the endo product is more thermodynamically favourable. This can be explained by the possible steric clash between bridging and terminal hydrogens in the Exo product. The steric clash in the Exo product raises the energy and hence leading the endo product being both kinetically and thermodynamically favourable.

: {{ steric clash picture, secondary orbital interaction picture}}
: {{ chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/http://www.cpp.edu/~psbeauchamp/pdf/316_MO_DA_rxn.pdf}}

= Exercise 3: Diels-Alder vs Cheletropic =

: In this exercise, the reaction between o-xylylene and sulphur dioxide is studied. Sulphur dioxide acts as the dienophile and reacts with o-xylylene via Hetero-Diels-Alder reaction with both endo and exo 6-membered ring products being formed. They can also react through cheletropic forming a 5-membered ring. The reaction scheme is shown below. With the semi-empirical PM6 methods all reactants, transition states and products are optimised. Reaction barriers and reaction energies are used to determine which reaction pathway is the most favourable.

:[[File:Xylylene and SO2 reaction scheme wcc14gee.png |500px|center|thumb|Figure 9: Reaction Scheme for O-Xylylene And Sulphur Dioxide]]

=== Intrinsic Reaction Coordinate Calculations Analysis ===

: IRC calculations are done in both directions from the transition state using the semi-empirical PM6 method. The results from the three different reaction pathways are summarised below.

:{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 5: IRC Caluclations and Total Energy along IRC for Different Pathways
! style="background: #0D4F8B; color: white;" | Pathway
! style="background: #0D4F8B; color: white;" | IRC
! style="background: #0D4F8B; color: white;" | Total Energy along IRC
|-
! Diels-Alder Reaction via Endo
| [[File:DA endo IRC move wcc14gee.gif|centre|500px]]
| [[File:Endo IRC energy path wcc14gee.PNG |centre|500px]]
|-
! Diels-Alder Reaction via Exo
| [[File:DA exo IRC move wcc14gee.gif|centre|500px]]
| [[File:Exo IRC energy path wcc14gee.PNG|centre|500px]]
|-
! Cheletropic Reaction
| [[File:Cheletropic IRC movie wcc14gee.gif|centre|500px]]
| [[File:Cheletropic IRC energy path wcc14gee.PNG|centre|500px]]
|}

=== Activation and Reaction Energies Analysis ===

: The energy of reactants, products and transition states are calculated by Gaussian and shown in Table 6. The energy of the reactants is the sum of the energies of o-xylylene and sulphur dioxide assuming that they are separated and have no interaction at the very beginning of the reaction. A reaction profile is produced using these data.

{| style="margin-left: auto; margin-right: auto; border: none;"
|
{|class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align:center"
|+ Table 4: Energies of Reactants, Transition States and Products for Both Endo and Exo Pathway
|-
! rowspan="2" style="background: #0D4F8B; color: white;" | Pathway
! colspan="5" style="background: #0D4F8B; color: white;" | Energy / kJ mol-1
|-
! style="background: #0D4F8B; color: white;" | Reactants
! style="background: #0D4F8B; color: white;" | Transition States
! style="background: #0D4F8B; color: white;" | Products
! style="background: #0D4F8B; color: white;" | Activation Energy
! style="background: #0D4F8B; color: white;" | Reaction Energy
|-
! style="background: #0D4F8B; color: white;" | Endo
| 157.92
| 237.76
| 56.99
| 79.84
| -100.94
|-
! style="background: #0D4F8B; color: white;" | Exo
| 157.92
| 241.75
| 56.32
| 83.82
| -101.60
|-
! style="background: #0D4F8B; color: white;" | Cheletropic
| 157.92
| 260.09
| 0.01
| 102.17
| -157.91
|}
|
|
|
|
| [[File:DA and cheletropic energy diagram wcc14gee.png |400px|centre|thumb|Figure 10: Reaction Profile of o-Xylylene and Sulphur Dioxide]]
|}

: From the reaction profile, the cheletropic product is the most stable and hence the cheletropic pathway is more thermodynamically favourable. This is because of the presence of the two strong S=O bonds and aromaticity.

: Diels-Alder reactions are more kinetically favoured compared to cheletropic reactions as they have lower activation energies. Similar to the reaction in exercise 2, the endo transition state is more stable than the exo transition state as the endo approach has secondary orbital interactions between the oxygens and o-xylylene p-orbitals. Due to the greater steric clash within the endo product, the exo product is more stable.

=== Instability of o-Xylylene ===
: [[File:Side reaction 2 wcc14gee.PNG|400px|right|thumb|Figure 11: Electrocyclic Reaction of o-Xylylene]]

: o-Xylylene is not following the Hückel rule (4n +2 electrons) so it does not have stabilisation from aromaticity, thus very unstable. During the reaction, the 6-membered ring of o-xylylene aromatises to form a benzene ring, hence the products gain stability from aromaticity and are thermodynamically more stable than the reactants.

: The formation of benzocylobutane through electrocyclic reaction is another reaction pathway that can happen apart from Diels-Alder and cheletropic reaction.

: The driving force for these reactions (Diels-Alder, cheletropic and electrocyclic) is the formation of the aromatic benzene ring, stabilising the reaction to become more thermodynamically favourable.

=== Side Reaction Analysis ===

: The internal cis-butadiene fragment in o-xylylene can also undergo Diels-Alder reaction forming both endo and exo products. The reaction scheme is shown below with the internal cis-butadiene fragment in light purple.

: [[File:OS reaction scheme wcc14gee.PNG |400px|centre|thumb|Figure 12: Diels-Alder Reaction between Internal Butadiene Fragment of o-Xylylene And Sulphur Dioxide]]

: Similar to the other reactions, the energies of the reactants, transition states and products are calculated and summarised in Table 7.

= Conclusion =

= References =