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File:THY-TS Ex2 Exo MO.png

2017-11-08T11:52:28Z

Hyt215: Hyt215 uploaded a new version of File:THY-TS Ex2 Exo MO.png

File:THY-TS Ex2 Endo MO.png

2017-11-08T11:51:08Z

Hyt215: Hyt215 uploaded a new version of File:THY-TS Ex2 Endo MO.png

Rep:TransitionStates-HYT215

2017-11-08T11:35:57Z

Hyt215: /* Extension */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that both the exo and endo product have steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
The transition states were optimised at the PM6 level and are shown below.
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due favourable seoncdary orbital interactions as discussed above.

The cheletropic product is the most stable and has the lowest reaction energy, and is the thermodynamic product. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially with the sulfur the sulfur atom. As sulfur is larger, the
anti-bonding interactions of its larger orbitals with surrounding oxygen decreases the stability of the Diels Alder products. There is little favourable bonding bonding interactions. However, the cheletropic HOMO consists of strong bonding interactions between the two pairs of carbons.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unstable. By comparing the HOMOs of the products in this exercise to the Diels Alder products of exercise 3, there are even more unfavourable interactions, especially between the carbon atoms. These probably account for the high energy levels of the product.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX4-exoHOMO.png|300px]]
|[[File:THY-TS-EX4-endoHOMO.png|300px]]
|}

== Conclusion ==
The optimisation and frequency calculations through computational chemistry allowed for the understanding of different reactions. Firstly, the visualisation of MOs of transition state in exercise 1 allowed for the conclusion that interacting MOs must have the same symmetry. The analysis of bond lengths in exercise 1 showed the importance of both hybridisation and bond order. The MO diagram of exercise 2 exemplified an inverse demand Diels Alder reaction, as compared to a normal Diels Alder in exercise 1. In both exercise 2, 3 and the extension, the competing reactions between Diels Alder exo and endo products and cheletropic products were analysed using the energy profile diagram. The importance of sterics and secondary orbital interactions in affecting the kinetic and thermodynamic products were also discussed.

File:THY-TS-EX4-endoHOMO.png

2017-11-08T11:24:57Z

Hyt215:

File:THY-TS-EX4-exoHOMO.png

2017-11-08T11:24:43Z

Hyt215:

File:THY-TS-31-PDT1.LOG

2017-11-08T11:16:12Z

Hyt215: Hyt215 uploaded a new version of File:THY-TS-31-PDT1.LOG

Rep:TransitionStates-HYT215

2017-11-08T11:06:39Z

Hyt215: /* Energy Calculations and Reaction Profile */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that both the exo and endo product have steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
The transition states were optimised at the PM6 level and are shown below.
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due favourable seoncdary orbital interactions as discussed above.

The cheletropic product is the most stable and has the lowest reaction energy, and is the thermodynamic product. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially with the sulfur the sulfur atom. As sulfur is larger, the
anti-bonding interactions of its larger orbitals with surrounding oxygen decreases the stability of the Diels Alder products. There is little favourable bonding bonding interactions. However, the cheletropic HOMO consists of strong bonding interactions between the two pairs of carbons.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
The optimisation and frequency calculations through computational chemistry allowed for the understanding of different reactions. Firstly, the visualisation of MOs of transition state in exercise 1 allowed for the conclusion that interacting MOs must have the same symmetry. The analysis of bond lengths in exercise 1 showed the importance of both hybridisation and bond order. The MO diagram of exercise 2 exemplified an inverse demand Diels Alder reaction, as compared to a normal Diels Alder in exercise 1. In both exercise 2, 3 and the extension, the competing reactions between Diels Alder exo and endo products and cheletropic products were analysed using the energy profile diagram. The importance of sterics and secondary orbital interactions in affecting the kinetic and thermodynamic products were also discussed.

Rep:TransitionStates-HYT215

2017-11-08T10:50:36Z

Hyt215: /* Optimised Transition States */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that both the exo and endo product have steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
The transition states were optimised at the PM6 level and are shown below.
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
The optimisation and frequency calculations through computational chemistry allowed for the understanding of different reactions. Firstly, the visualisation of MOs of transition state in exercise 1 allowed for the conclusion that interacting MOs must have the same symmetry. The analysis of bond lengths in exercise 1 showed the importance of both hybridisation and bond order. The MO diagram of exercise 2 exemplified an inverse demand Diels Alder reaction, as compared to a normal Diels Alder in exercise 1. In both exercise 2, 3 and the extension, the competing reactions between Diels Alder exo and endo products and cheletropic products were analysed using the energy profile diagram. The importance of sterics and secondary orbital interactions in affecting the kinetic and thermodynamic products were also discussed.

Rep:TransitionStates-HYT215

2017-11-08T10:49:35Z

Hyt215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that both the exo and endo product have steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
The optimisation and frequency calculations through computational chemistry allowed for the understanding of different reactions. Firstly, the visualisation of MOs of transition state in exercise 1 allowed for the conclusion that interacting MOs must have the same symmetry. The analysis of bond lengths in exercise 1 showed the importance of both hybridisation and bond order. The MO diagram of exercise 2 exemplified an inverse demand Diels Alder reaction, as compared to a normal Diels Alder in exercise 1. In both exercise 2, 3 and the extension, the competing reactions between Diels Alder exo and endo products and cheletropic products were analysed using the energy profile diagram. The importance of sterics and secondary orbital interactions in affecting the kinetic and thermodynamic products were also discussed.

Rep:TransitionStates-HYT215

2017-11-08T10:47:20Z

Hyt215: /* Conclusion */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
The optimisation and frequency calculations through computational chemistry allowed for the understanding of different reactions. Firstly, the visualisation of MOs of transition state in exercise 1 allowed for the conclusion that interacting MOs must have the same symmetry. The analysis of bond lengths in exercise 1 showed the importance of both hybridisation and bond order. The MO diagram of exercise 2 exemplified an inverse demand Diels Alder reaction, as compared to a normal Diels Alder in exercise 1. In both exercise 2, 3 and the extension, the competing reactions between Diels Alder exo and endo products and cheletropic products were analysed using the energy profile diagram. The importance of sterics and secondary orbital interactions in affecting the kinetic and thermodynamic products were also discussed.

Rep:TransitionStates-HYT215

2017-11-08T10:29:12Z

Hyt215: /* Introduction */

==Introduction==
The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

As the potential energy is work done over distance: <math>V = \int F \mathrm{d}x</math>

Therefore: <math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math>, where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2}</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer leo nunc, ornare vehicula augue quis, venenatis tincidunt enim. Pellentesque sed metus sit amet nisl vulputate feugiat vitae aliquam leo. Nam pretium enim libero, vitae rutrum elit lobortis in. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Nullam ac lorem felis. Vivamus eget diam laoreet, congue eros vitae, consectetur quam. Vestibulum quis posuere ante. Proin at dui vel nunc condimentum porttitor tempus vitae nisi. Donec feugiat ultrices mauris eget commodo. Donec fermentum sem ut metus placerat, id vulputate libero tempus.

Rep:TransitionStates-HYT215-intro

2017-11-08T10:17:46Z

Hyt215:

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

<math>V = -\int F \mathrm{d}x</math>

<math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math> where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2},\!\</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

Rep:TransitionStates-HYT215-intro

2017-11-08T10:16:56Z

Hyt215:

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

<math>V = -\int F \mathrm{d}x</math>

<math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency: <math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math> where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2},\!\,</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Through Gaussian calculations, the reactants, transition states and products were optimised. All calculations were done at PM6 level except exercise 2 where the optimised PM6 structures were further optimised at B3LYP 6-31G(d) level. From these optimisations, the molecular orbitals, bonds lengths and intrinsic reaction coordinates could be obtained and analysed. The thermodynamic data from Gaussian calculations were also used to support the analysis on competing reactions for Exercise 2, Exercise 3 and the extension.

Rep:TransitionStates-HYT215-intro

2017-11-08T10:09:07Z

Hyt215:

In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

The potential energy surface (PES) represents the potential energy of the molecule visualised along two dimensions. The potential energy is a function of 3N-6 independent nuclear coordinates where <math>E=f(q_1, q_2,q_3, ... ,q_{3N-6})</math>. If the energy is plotted only along one dimension, an energy profile is obtained. This can also be obtained by taking a vertical slice of the PES. When the first derivative of the PES is zero <math>(\tfrac{\partial E(q_1)}{\partial q_1}=0)</math>, it corresponds to a minimum, maximum or saddle point. To better understand the nature of these points, the second derivative <math>(\tfrac{\partial E^2}{\partial q_1^2})</math>, corresponding to the frequency is calculated. If this value is positive, it is the minimum of the PES. This typically corresponds to reactant or products. If the value is negative, it could be a saddle point which corresponds to the transition state of a molecule. As the bonds can be approximated to a harmonic oscillator, it obeys Hooke's law where:

<math>F=kx</math>

<math>V = -\int F \mathrm{d}x</math>

<math>V= \tfrac{1}{2}kx^2</math>

<math> k = \tfrac{\partial E^2}{\partial q_1^2} </math>

We can thus solve for the frequency:
<math> \nu = {1\over {2 \pi}} \sqrt{k \over \mu} </math> where: <math>\mu = \cfrac{m_1 m_2}{m_1 + m_2},\!\,</math>

The above calculations are valid due to Born-Oppenheimer approximation, where the electronic distribution of a molecule adjust instantaneously to the movement of a nuclei and that the energy is a function of nuclei positions, where nuclear kinetic energy is not taken into account.

Rep:TransitionStates-HYT215-intro

2017-11-08T09:24:24Z

Hyt215: Created page with "In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at..."

Rep:TransitionStates-HYT215

2017-11-08T02:12:40Z

Hyt215: /* Conclusion */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2-DIRECTTS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Optimised Product
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-31-PDT1.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-32-PDT2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer leo nunc, ornare vehicula augue quis, venenatis tincidunt enim. Pellentesque sed metus sit amet nisl vulputate feugiat vitae aliquam leo. Nam pretium enim libero, vitae rutrum elit lobortis in. Vestibulum ante ipsum primis in faucibus orci luctus et ultrices posuere cubilia Curae; Nullam ac lorem felis. Vivamus eget diam laoreet, congue eros vitae, consectetur quam. Vestibulum quis posuere ante. Proin at dui vel nunc condimentum porttitor tempus vitae nisi. Donec feugiat ultrices mauris eget commodo. Donec fermentum sem ut metus placerat, id vulputate libero tempus.

Rep:TransitionStates-HYT215

2017-11-08T02:08:53Z

Hyt215: /* Extension */

File:THY-TS-32-PDT2-DIRECTTS.LOG

2017-11-08T02:06:41Z

Hyt215:

File:THY-TS-32-PDT2.LOG

2017-11-08T02:05:17Z

Hyt215:

File:THY-TS-31-PDT1-DIRECTTS.LOG

2017-11-08T02:01:15Z

Hyt215:

File:THY-TS-31-PDT1.LOG

2017-11-08T02:00:55Z

Hyt215:

Rep:TransitionStates-HYT215

2017-11-08T01:57:41Z

Hyt215: /* Energy Calculations and Reaction Profile */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have some steric clashes, especially from the sulfur atom. As sulfur is larger, its
anti-bonding interactions with surrounding oxygen decreases the stability of the product. The cheletropic HOMOs look extremely stable and has little contributions from the sulfur.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-08T01:52:08Z

Hyt215: /* Energy Calculations and Reaction Profile */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have steric clashes.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
|'''HOMOs of Optimised Products'''
|[[File:THY-TS-EX3-EXO.png|300px]]
|[[File:THY-TS-EX3-Endo.png|300px]]
|[[File:THY-TS-EX3-chela.png|300px]]
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

File:THY-TS-EX3-chela.png

2017-11-08T01:47:07Z

Hyt215:

File:THY-TS-EX3-Endo.png

2017-11-08T01:46:47Z

Hyt215:

File:THY-TS-EX3-EXO.png

2017-11-08T01:46:07Z

Hyt215:

File:THY-TS-EX3-chela-MO2.log

2017-11-08T01:29:14Z

Hyt215:

Rep:TransitionStates-HYT215

2017-11-07T23:53:33Z

Hyt215: /* Energy Calculations and Reaction Profile */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have steric clashes.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!HOMOs of Optimised Products
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-EX3-EXO-MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 138; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-EX3-ENDO-MO3.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-EX3-chela-MO.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

File:THY-TS-EX3-chela-MO.log

2017-11-07T23:49:30Z

Hyt215:

File:THY-TS-EX3-ENDO-MO3.log

2017-11-07T23:49:13Z

Hyt215:

File:THY-TS-EX3-EXO-MO.log

2017-11-07T23:48:29Z

Hyt215:

Rep:TransitionStates-HYT215

2017-11-07T23:38:42Z

Hyt215: /* Energy Calculations and Reaction Profile */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]

The endo Diels Alder product is kinetically favoured as it has the lowest reaction barrier, probably due to steric interactions. The cheletropic product is the most stable and has the lowest reaction energy. In the cheletropic form, the molecule is able to adopt a planar configuration, and maximise the distance between the oxygen atoms and the neighbouring hydrogen atoms. It can be seen from the HOMOs below that the Diels Alder products both have steric clashes.

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!HOMOs of Optimised Products
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 38; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-29-3-EXO.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 148; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 118; mo 29; zoom 0; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-22-CHELA-PRODUCT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

File:THY-TS-16.LOG

2017-11-07T23:27:19Z

Hyt215:

File:THY-TS-29-3-EXO.LOG

2017-11-07T23:21:24Z

Hyt215:

File:THY-TS-22-CHELA-PRODUCT.LOG

2017-11-07T23:20:47Z

Hyt215:

File:THY-TS-26-3exo-HPC.log

2017-11-07T23:20:16Z

Hyt215:

File:THY-TS-19-ENDO-631.LOG

2017-11-07T23:18:44Z

Hyt215: Hyt215 uploaded a new version of File:THY-TS-19-ENDO-631.LOG

File:THY-TS-20-EXO-631.LOG

2017-11-07T23:18:25Z

Hyt215: Hyt215 uploaded a new version of File:THY-TS-20-EXO-631.LOG

Rep:TransitionStates-HYT215

2017-11-07T23:04:05Z

Hyt215: /* Energy Calculations */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}

Due to the reaction energy being lower, the endo product is also thermodynamically favoured. Typically, the exo product is thermodynamically preferred as the endo product is likely to have diaxial interactions. However, it is observed that the exo product also has steric clashes.

As the reaction barrier is lower for the endo product, it is kinetically favoured. This is due to secondary interactions between the oxygen atom on the 1,3-dioxole with the 1,3-cyclohexdiene, which will be further elaborated. The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.

{| class="wikitable"
!
!Exo
!Endo
|-
!Product
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-EXO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01;set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-631.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-

!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

File:THY-TS-20-EXO-631.LOG

2017-11-07T22:48:12Z

Hyt215:

File:THY-TS-19-ENDO-631.LOG

2017-11-07T22:47:59Z

Hyt215:

Rep:TransitionStates-HYT215

2017-11-07T22:32:31Z

Hyt215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:32:13Z

Hyt215: /* Reaction Path */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.
<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:30:59Z

Hyt215: /* Molecular Orbitals of Transition States */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="6" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}

=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:28:46Z

Hyt215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===

{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:27:16Z

Hyt215: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''Optimised'''
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:19:48Z

Hyt215: /* Molecular Orbitals of Transition State */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition State
|-
|'''Optimised'''
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:17:21Z

Hyt215: /* Molecular Orbitals of transition State */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of Transition State ===
Through computational methods done at PM6 level, the transition states, along with HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised TS'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised TS'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="4" |Transition State
|-
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:16:28Z

Hyt215: /* Molecular Orbitals of transition State */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of transition State ===
Through computational methods done at PM6 level, the HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''Optimised TS'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''Optimised TS'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="4" |Transition State
|-
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==

Rep:TransitionStates-HYT215

2017-11-07T22:14:15Z

Hyt215: /* Exercise 3: Diels-Alder vs Cheletropic */

== Introduction ==
* you will have explored advanced techniques in Gaussian, a computational chemistry program, and GaussView, the graphical user interface for Gaussian.
* you should be able to explain what a Transition State and a Potential Energy Surface are.
* you should be able to use chemical intuition to help you to locate stationary points on a Potential Energy Surface.
* you should be able to discuss the roles of sterics and secondary orbital interactions in determining the kinetic and thermodynamic products of a reaction.
* In your introduction, briefly describe what is meant by a minimum and transition state in the context of a potential energy surface. What is the gradient and the curvature at each of these points? (for thought later on, how would a frequency calculation confirm a structure is at either of these points?)

== Exercise 1: Reaction of Butadiene with Ethylene ==
The Diels-Alder reaction of butadiene with ethylene to give cyclohexene is an example of a Diels-Alder reaction. It is a [4+2] cycloaddition between a conjugated diene (butadiene) and dienophile (ethylene), with the reaction scheme given below.[[File:THY-TS Ex1.png|none|thumb|Reaction scheme of butadiene with ethylene to form cyclohexene]]

=== Molecular Orbitals of transition State ===
Through computational methods done at PM6 level, the HOMOs and LUMOs of the two reactants were obtained as shown below.

{| class="wikitable"
! colspan="2" |Butadiene
! colspan="2" |Ethene
|-
|'''MO 12'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 7'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''MO 11'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|'''MO 6'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The interaction of the above four MOs during the transition state gave the four MOs below.
{| class="wikitable"
! colspan="4" |Transition State
|-
|'''MO 16'''
|'''MO 17'''
(HOMO)
|'''MO 18'''
(LUMO)
|'''MO 19'''
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

By observing the interactions of the orbitals and using the relative energy levels found from the calculations, the MO diagram of the transition state is given below. It is also noted that for the orbitals to interact, they must have the same symmetry labels. If not, the reaction would be forbidden.
[[File:THY-TS Ex1 MO.png|none|thumb|636x636px]]

The antisymmetric HOMO of butadiene (MO 11) interacts with the antisymmetric LUMO of ethylene (MO 7) to give the two antisymmetric MOs, bonding orbital MO 16 and anti-bonding MO 19 of the cyclohexene transition state. The symmetric LUMO of butadiene (MO 12) interacts with the symmetric HOMO of ethylene (MO 6) to give the two symmetric MOs, bonding orbital MO 17 and anti-bonding MO 18 of the cyclohexene transition state.

Hence, it is concluded that for a symmetric-symmetric or antisymmetric-antisymmetric interaction, the orbital overlap integral is non-zero. However, a symmetric-antisymmetric interaction would be zero.

=== Bond Lengths ===
{| class="wikitable"
!
!Jmol
!Bond Lengths (unit)
|-
|'''Butadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-BUTA2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C1-C9: 1.33 Å

C9-C7: 1.47 Å

C7-C4: 1.33 Å
|-
|'''Ethylene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 4 1; select atomno=[4 1]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-ETHENE2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C4: 1.33 Å
|-
|'''Transition State'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 14; measure 1 11; measure 4 14; measure 11 14; measure 4 7; measure 7 9; measure 9 1; select atomno=[4 7 9 1 11 14]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|C1-C9: 1.38 Å

C9-C7: 1.41 Å

C7-C4: 1.38 Å

C4-C14: 2.11 Å

C14-C11: 1.38 Å

C11-C1: 2.11 Å
|-
|'''Cyclohexene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; measure 1 2; measure 2 3; measure 3 4; measure 4 5; measure 5 6; measure 6 1; select atomno=[1 2 3 4 5 6]; label display; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-24-CYCLOHEXENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|C3-C4: 1.50 Å

C4-C5: 1.34 Å

C5-C6: 1.50 Å

C6-C1: 1.54 Å

C1-C2: 1.53 Å

C2-C3: 1.54 Å
|}

The two double bonds of the butadiene increase from 1.33 Å to 1.38 Å in the transition state and then to 1.50 Å in the product. These bonds were initially sp<sup>2</sup>-sp<sup>2 </sup>C-C double bonds which lengthened to form the sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds.

The single bond of butadiene decreased from 1.47 Å to 1.41 Å in the transition state and then to 1.34 Å in the final product. The bond was initially sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond which shortened to form the sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond.

The double bond of ethylene increased from 1.33 Å to 1.38 Å in the transition state and then to 1.54 Å in the product. The bond was a sp<sup>2</sup>-sp<sup>2 </sup>C-C double bond which lengthened to form a sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

The bond formation between butadiene and ehtylene was reflected in the decrease in the distance of 2.11 Å during the transition state to 1.54 Å in the product, typical of the sp<sup>3</sup>-sp<sup>3 </sup>C-C single bond.

It is noted that the lengths of the C-C single bonds are dependent on the amount of s character. The higher the s character of the orbitals, the shorter the bond. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds are longer than the are sp<sup>3</sup>-sp<sup>2 </sup>C-C single bonds, which is also longer than the sp<sup>2</sup>-sp<sup>2 </sup>C-C single bonds. sp<sup>2</sup>-sp<sup>2 </sup>carbons with a higher bond order of two has a shorter length than that of one.

The double bonds of butadiene, ethylene and cyclohexene correspond closely to literature values of alkene of 1.34 Å. The sp<sup>3</sup>-sp<sup>2 </sup>C-C single bond of cyclohexene also corresponds to the literature value of 1.50 Å. The sp<sup>2</sup>-sp<sup>2 </sup>C-C single bond of butadiene also corresponds to the literature value of 1.47 Å. The sp<sup>3</sup>-sp<sup>3 </sup>C-C single bonds of cyclohexene also correspond to the literature value of 1.54 Å. <ref>Fox, Marye Anne; Whitesell, James K. (1995). ''Organische Chemie: Grundlagen, Mechanismen, Bioorganische Anwendungen''. Springer.</ref> The distance between the two carbons forming the bond of 2.11 Å is smaller than two times the length of the van der Waals radius of carbon (3.4 Å), indicating bond forming or breaking in the transition state.<ref>Bondi, A. (1964). "Van der Waals Volumes and Radii". ''J. Phys. Chem.'' '''68''' (3): 441–451. doi:10.1021/j100785a001</ref>

=== Reaction Path ===
The vibration below shows the reaction path at the transition state. As the bond formation between the diene and dienophile took place simultaneously, this bond formation is synchronous.

<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 15; vibration 2; mo nodots nomesh fill translucent; mo titleformat ""; zoom0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-18-COMBINE2-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

== Exercise 2: Reaction of Cyclohexadiene and 1,3-Dioxole ==
[[File:THY-TS Ex2 Reaction Scheme reupload.png|none|thumb|575x575px]]
Continuing from the previous exercise, this section explores another Diels-Alder between a cyclohexadiene and 1,3-dioxole where dioxole is the dienophile, with the reaction scheme given below. As the dienophile is now substituted, the direction of approach of dioxole would affect the stereochemistry of the product formed, either an endo- or exo- product.

=== Molecular Orbitals of Transition States ===
Through computational methods done at B3LYP 6-31G(d) level, the HOMOs and LUMOs of the two reactants were obtained as shown below
{| class="wikitable"
! colspan="2" |1,3-cyclohexadiene
! colspan="2" |1,3-dioxole
|-
|'''MO 23'''
(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 20'''

(LUMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|-
|'''MO 22'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 18; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-25-CYCLOHEXADIENE-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|'''MO 19'''
(HOMO)
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-21-DIOXOLE-631-DISPLACEMENT2.LOG </uploadedFileContents>
</jmolApplet>
</jmol>

|}
The interaction of the above four MOs during the transition state for both endo and exo products gave the four MOs below.
{| class="wikitable"
! colspan="5" |Transition States
|-
|
|'''MO 40'''
|'''MO 41'''
(HOMO)
|'''MO 42'''
(LUMO)
|'''MO 43'''
|-
|'''Exo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''Endo'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
Using the energy levels of MOs derived from the calculations, the following MO diagram was obtained. For a normal Diels-Alder reaction, as shown in exercise 1, the diene is electron rich and has a higher HOMO than the dienophile, which is electron poor. However, in this inverse demand Diels Alder reaction, 1,3-dioxole is an electron rich dienenophile and has a higher HOMO than the cyclohexadiene. This occurs due to the presence of electron rich oxygen atoms adjacent to the C-C double bond on 1,3-dioxole. The electron donating effect of the oxygen atoms lead to 1,3-dioxole having a higher HOMO.

{| class="wikitable"
!Exo
!Endo
|-
|[[File:THY-TS Ex2 Exo MO.png|frameless|658x658px]]
|[[File:THY-TS Ex2 Endo MO.png|frameless|678x678px]]
|}
=== Energy Calculations ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!'''1,3-cyclohexadiene'''
|<nowiki>-6.1259 × 10</nowiki><sup>5</sup>
|-
!'''1,3-dioxole'''
|<nowiki>-7.0119 × 10</nowiki><sup>5</sup>
|-
!'''Sum of Reactants'''
|<nowiki>-1.3138 × 10</nowiki><sup>6</sup>
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|<nowiki>-1.313614 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313845 × 10</nowiki><sup>6</sup>
|167.71
|<nowiki>-63.744</nowiki>
|-
!'''Endo'''
|<nowiki>-1.313621 × 10</nowiki><sup>6</sup>
|<nowiki>-1.313849 × 10</nowiki><sup>6</sup>
|159.88
|<nowiki>-67.334</nowiki>
|}
As the reaction barrier is lower for the endo product, it is kinetically favoured. Due to the reaction energy being lower, the endo product is also thermodynamically favoured.

The HOMO of the transition states were also analysed in greater detail. When the mo cutoff was decrease to 0.01, the interactions for the p-orbitals that were expected from the HOMO (MO 41) of the exo transition state is now clearer as compared to when the isovalue was 0.02 (as seen above). For the HOMO of the endo transition state, there are secondary interactions, further stabilising the transition state, thus lowering its energy. The interactions have now been drawn into the schematic diagram of MO 41 in the table below. These favourable secondary interactions were not observed for the HOMO of the exo transition state. This is probably why the endo product is kinetically favoured over the exo product.
{| class="wikitable"
!
!Exo
!Endo
|-
!HOMO at isovalue=0.01
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 20; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-20-exo-TS-631-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 30; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; mo cutoff 0.01; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-19-ENDO-TS-631.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Schematic
|[[File:THY-TS_Ex2_Exo_MO41.png|center|125px]]
|[[File:THY-TS_Ex2_Endo_MO41.png|center|125px]]
|}

== Exercise 3: Diels-Alder vs Cheletropic ==
Similar to exercise 2, the competing reactions between o-xylylene and SO<sub>2</sub> were examined. Firstly, there are two possible Diels-Alder products, endo and exo. Secondly, there is an additional cheletropic reaction that could take place where the sulfur atom forms a five-membered ring with o-xylylene. These products are shown in the scheme below.
[[File:THY-TS Ex3 Reaction Scheme.png|none|thumb|600x600px|Reaction scheme between sulfur dioxide and o-xylylene to give endo and exo Diels Alder as well as cheletropic product]]

=== Optimised Transition States ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!IRC Coordinates
|[[File:THY-TS-EX3-EXO-IRC.gif]]
|[[File:THY-TS-EX3-ENDO-IRC.gif]]
|[[File:THY-TS-EX3-CHELA-IRC.gif]]
|-
!IRC Files
![[:File:THY-TS-26-3exo-freeze4-TS-IRC-HPC.log |IRC File]]
![[:File:THY-TS-23-CHELA-FREEZEOPT-TS-IRC.LOG|IRC File]]
![[:File:THY-TS-16D.LOG|IRC File]]
|}

=== Energy Calculations and Reaction Profile ===
The following calculations of the reactants, transition states and products of both exo and endo Diels Alder and chelatropic products were carried out at PM6 level and tabulated below.
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|241.75
|56.330
|83.318
|<nowiki>-102.10</nowiki>
|-
!'''Endo'''
|237.77
|56.976
|79.339
|<nowiki>-101.46</nowiki>
|-
!Cheletropic
|260.08
|<nowiki>-0.0052510</nowiki>
|101.65
|<nowiki>-158.44</nowiki>
|}
From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:Free energy of DA.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products and the cheletropic product]]
Discuss the different activation energies

=== IRC ===
{| class="wikitable"
!
!Diels-Alder (Exo)
!Diels-Alder (Endo)
!Cheletropic
|-
!Optimised TS
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-26-3exo-freeze4-TS-HPC.log</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 14; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-16C.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
!<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>THY-TS-23-CHELA-FREEZEOPT-TS.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
From the IRC shown above, the 6-membered ring of o-xylylene initially consisted of 4 C-C single bonds and 2 C-C double bonds. After the reaction, the 6-membered ring gained stability through aromaticity.

== Extension ==
As o-xylylene contains two diene fragments suitable to undergo a Diels-Alder reaction, this section will move on to explore the reaction profile of this reaction relative to exercise 3. The reaction scheme is shown below.
[[File:THY-TS Ex4 Reaction Scheme.png|none|thumb|400x400px|Reaction scheme of sulfure dioxide undergoing Diels Alder with the second cis-butadiene fragment on o-xylylene]]

=== Energy Calculations and Reaction Profile ===
{| class="wikitable"
!
!Energy/ kJmol<sup>-1</sup>
|-
!o-Xylylene
|469.85
|-
!'''SO<sub>2</sub>'''
|<nowiki>-311.42</nowiki>
|-
!'''Sum of Reactants'''
|158.43
|}
{| class="wikitable"
! rowspan="2" |
! colspan="4" |Energy/ kJmol<sup>-1</sup>
|-
!'''''Transition State'''''
!'''''Product'''''
!'''''Reaction Barrier'''''
!'''''Reaction Energy'''''
|-
!'''Exo'''
|242.58
|176.71
|117.39
|18.276
|-
!'''Endo'''
|267.98
|172.26
|109.55
|13.829
|}

From the calculations, the reaction profile was derived and plotted on'' ''Microsoft Excel.[[File:THY-TS-Energy_Profile_extra.png|none|thumb|433x433px|Reaction profile to of both the endo and exo Diels Alder products of sulfur reacting with the second cis-butadiene fragment]]As the activation energy for both the exo and endo product is higher than that of the reaction on the other cis-butadiene fragment site, this site of reaction is less kinetically favourable. The reaction energy is also slightly positive in this case, as compared to negative values in the exercise 3. This shows that the products formed are more unstable than the reactants, and is thermodynamically unfavourable.

== Conclusion ==