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Rep:MOD:JDN15Y3lab

2018-03-08T15:45:04Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate. DFT calculations define the energy of a system as a sum of 6 components, E<sub>DFT</sub> = E<sub>NN</sub> + E<sub>T</sub> + E<sub>V</sub> + E<sub>Coul</sub> + E<sub>Exchange</sub> + E<sub>Corr</sub>.

E<sub>NN</sub> = nuclear-nuclear repulsion, E<sub>V</sub> = nuclear-electron attraction, E<sub>Coul</sub> = electron-electron Coloumb repulsion.

These terms above are the same used in the Hartree-Fock theory. The energies below are different from the terms used in the Hartree-Fock theory as E<sub>Corr</sub> is not accounted for in the theory.

E<sub>T</sub> = kinetic energy of the electrons, E<sub>Exchange</sub> = electron-electron exchange energies, E<sub>Corr</sub> = correlated movement of electrons of different spin.

B3LYP (Becke-3-LFP) is a hybrid method, which mixing exchange energies calculated in an exact manner with those obtained from DFT methods to improve performance.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

[[File:JDN15EXOClash.png| centre |300px]]

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.
===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}
===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

Comparing the values from the table, we can see that both exo and endo for this Diels-Alder reaction has a much higher reaction barrier than the previous reactions (discussed earlier). Hence the secondary Diels-Alder reactions are the least kinetically favourable. We can also see that the reaction energies of the secondary Diels-Alder reactions are positive, indicating that the reaction is highly thermodynamically unfavourable as ΔG>0 and hence the reaction is not spontaneous.

==Conclusion==
Gaussian is a useful method to carry out molecular geometry optimisations and calculations. By investigating the free energies of the transition states and products, we can determine the reaction energies and reaction barriers of the reaction. We can then determine which reactions are kinetically or thermodynamically favoured. This computational method is a powerful tool that can be used for preliminary research before testing out the reactions experimentally. It also provides a visual representation that allows better understanding on the interactions between the MOs of the molecules before, during and after the reaction.

Rep:MOD:JDN15Y3lab

2018-03-08T15:00:39Z

Jdn15: /* Cis-butadiene Fragment on Xylylene for Reactions */

Rep:MOD:JDN15Y3lab

2018-03-08T14:55:18Z

Jdn15: /* Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole */

File:JDN15EXOClash.png

2018-03-08T14:51:14Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-08T14:31:46Z

Jdn15: /* Gaussview tool used for calculations */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate. DFT calculations define the energy of a system as a sum of 6 components, E<sub>DFT</sub> = E<sub>NN</sub> + E<sub>T</sub> + E<sub>V</sub> + E<sub>Coul</sub> + E<sub>Exchange</sub> + E<sub>Corr</sub>.

E<sub>NN</sub> = nuclear-nuclear repulsion, E<sub>V</sub> = nuclear-electron attraction, E<sub>Coul</sub> = electron-electron Coloumb repulsion.

These terms above are the same used in the Hartree-Fock theory. The energies below are different from the terms used in the Hartree-Fock theory as E<sub>Corr</sub> is not accounted for in the theory.

E<sub>T</sub> = kinetic energy of the electrons, E<sub>Exchange</sub> = electron-electron exchange energies, E<sub>Corr</sub> = correlated movement of electrons of different spin.

B3LYP (Becke-3-LFP) is a hybrid method, which mixing exchange energies calculated in an exact manner with those obtained from DFT methods to improve performance.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.
===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}
===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

Rep:MOD:JDN15Y3lab

2018-03-08T13:49:45Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}
By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.
===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP2.png|centre|600px]]

Based on the data from the table, we can calculate that the Cheletropic product has the lowest energy and hence is thermodynamically favoured. As sulfur is larger than C, the resulting twist in the 6 membered ring in the Diels-Alder products have a ring strain due to inefficient sp<sup>3</sup> hybridisation, resulting in a highly distorted structure. This is in comparison to the Cheletropic product, which is able to adopt a planar configuration that maximises the distance between the O and the neighbouring H atoms. However, the Cheletropic reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

From the transition state HOMO, we can observe that both the endo and exo TS have stabilising secondary orbital interactions, therefore reducing the reaction barrier in these reactions. This also explains why the energy of the exo and endo TS are relatively close in energy. We can also see that the Cheletropic TS has no stabilising secondary interactions and is highly antisymmetric with many nodes, resulting a higher energy TS.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!rowspan="2" style="text-align: center;"|
! colspan="2" style="text-align: center;"| Diels-Alder Reaction
!rowspan="2" style="text-align: center;"| Cheletropic Reaction
|-
!style="text-align: center;"| ENDO
!style="text-align: center;"| EXO
|-
|style="text-align: center;"|Transition State
HOMO
| [[File:JDN15EXOHOMO.png]]
| [[File:JDN15ENDOHOMO.png]]
| [[File:JDN15CHEHOMO.png]]
|}
===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)
!File Logs

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.105054
|style="text-align: center;" | 0.067300
|style="text-align: center;" | 119.8
|style="text-align: center;" | 20.7
|style="text-align: center;" | [[File:JDN15_EXO2_Product.LOG]]
[[File:JDN15_EXO_TS2.LOG]]
|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" | 0.102070
|style="text-align: center;" | 0.065612
|style="text-align: center;" | 112.0
|style="text-align: center;" | 16.3
|style="text-align: center;" | [[File:JDN15_ENDO2_Product.LOG]]
[[File:JDN15_ENDO2_TS.LOG]]
|}

File:JDN15 ENDO2 Product.LOG

2018-03-08T13:48:24Z

Jdn15:

File:JDN15 ENDO2 TS.LOG

2018-03-08T13:47:43Z

Jdn15:

File:JDN15 EXO TS2.LOG

2018-03-08T13:45:05Z

Jdn15:

File:JDN15 EXO2 Product.LOG

2018-03-08T13:40:46Z

Jdn15:

File:JDN15RP2.png

2018-03-08T13:04:45Z

Jdn15:

File:JDN15CHEHOMO.png

2018-03-08T12:55:17Z

Jdn15:

File:JDN15ENDOHOMO.png

2018-03-08T12:54:42Z

Jdn15:

File:JDN15EXOHOMO.png

2018-03-08T12:54:06Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-08T12:12:28Z

Jdn15: /* Reaction Barrier and and Reaction Energy Calculations */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy. <br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |

|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|}

Rep:MOD:JDN15Y3lab

2018-03-08T12:09:28Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15RP.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |

|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|}

File:JDN15RP.png

2018-03-08T12:07:14Z

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Rep:MOD:JDN15Y3lab

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Jdn15: /* Introduction */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, replacing the two-electron integrals, Coulomb and exchange integrals, which are more difficult to calculate.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15Rxn_Profile.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |

|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|}

Rep:MOD:JDN15Y3lab

2018-03-08T11:28:47Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15Rxn_Profile.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA 2'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |

|-
|style="text-align: center;" |'''ENDO DA 2'''
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|style="text-align: center;" |
|}

Rep:MOD:JDN15Y3lab

2018-03-08T11:06:21Z

Jdn15: /* Cis-butadiene Fragment on Xylylene for Reactions */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15Rxn_Profile.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

Rep:MOD:JDN15Y3lab

2018-03-07T18:00:01Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15Rxn_Profile.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene. Therefore, it is likely the endo Diels-Alder product forms as the major product under low temperatures and short reaction times in non-equilibrating conditions.

By observing the visual animations of the IRCs, it is observed that the 6 membered ring in Xylyene which originally had 4 sp<sup>3</sup> C and 2 sp<sup>2</sup> C gained stability by attaining aromaticity after the reaction, forming 6 sp<sup>2</sup> C.

===Cis-butadiene Fragment on Xylylene for Reactions===

There are 2 cis-butadiene fragments on Xylylene which is able to undergo reactions. The outer cis-butadiene is able to undergo Diels-Alder reactions and Cheletropic reactions as seen above, while the inner cis-butadiene fragment is only able to undergo Diels-Alder reaction. However, reaction at this site is highly unfavoured due to steric hinderance and the formation of a strained bicyclic ring. Moreover, this reaction not only provides no aromatic stabilisation to the system, it lowers the conjugated system and hence is highly unfavoured.

[[File:JDN15EX3RXN2.png|centre|500px]]

File:JDN15EX3RXN2.png

2018-03-07T17:57:08Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T17:20:37Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|style="text-align: center;" |'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|style="text-align: center;" |'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|style="text-align: center;" |'''Cheletropic Reaction'''
|[[File:JDN15CHETSV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.059417
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 85.7
|style="text-align: center;" | -99.7

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 81.8
|style="text-align: center;" | -99.3

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.0
|}

From the table above, a reaction profile for reach of the reactions was constructed.

[[File:JDN15Rxn_Profile.png|centre|600px]]

Based on the data from the table, we can calculate that the cheletropic product has the lowest energy and hence is thermodynamically favoured. This may be due to the product being able to adop a planar configuration that maximises the distance between the O and the neighbouring H atoms. Also, there may be formation of a less strained ring as S is larger than C. However, the reaction also has the highest reaction barrier, suggesting it is the least kinetically favoured pathway. Therefore, it is likely the cheletropic product forms as the major product under high temperatures and long reaction times in equilibrating conditions.

The endo Diels-Alder product is kinetically favoured as it has the lowest reaction barrier. The endo product has a lower reaction barrier than the exo product, which is likely due to additional stabilising interactions between the p orbitals on the O of SO<sub>2</sub> and the conjugated π system on xylylene.

File:JDN15Rxn Profile.png

2018-03-07T16:49:04Z

Jdn15:

File:Rxn Profile.png

2018-03-07T16:47:39Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T16:12:05Z

Jdn15: /* Reaction Barrier and and Reaction Energy Calculations */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|rowspan="2" style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CHEV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.060149
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 83.8
|style="text-align: center;" | -101.6

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 79.8
|style="text-align: center;" | -101.0

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.9
|}

File:JDN15CHETSV.gif

2018-03-07T16:10:54Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T16:10:24Z

Jdn15: /* Reaction Energy and Reaction Barrier Calculations */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Barrier and and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CHEV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.060149
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 83.8
|style="text-align: center;" | -101.6

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 79.8
|style="text-align: center;" | -101.0

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.9
|}

Rep:MOD:JDN15Y3lab

2018-03-07T16:08:45Z

Jdn15: /* Exercise 3: Diels-Alder vs Cheletropic */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Energy and Reaction Barrier Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CHEV.gif]]
|[[File:JDN15CHETS2.LOG]]
[[File:JDN15CHENP2.LOG]]
|}

===Reaction Barrier and Reaction Energy Calculations===
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|rowspan="3" style="text-align: center;" | 0.060149
|style="text-align: center;" | 0.092077
|style="text-align: center;" | 0.021451
|style="text-align: center;" | 83.8
|style="text-align: center;" | -101.6

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | 0.090559
|style="text-align: center;" | 0.021698
|style="text-align: center;" | 79.8
|style="text-align: center;" | -101.0

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | 0.099062
|style="text-align: center;" | 0.000005
|style="text-align: center;" | 102.2
|style="text-align: center;" | -157.9
|}

File:JDN15CHETS2.LOG

2018-03-07T16:01:49Z

Jdn15:

File:JDN15CHENP2.LOG

2018-03-07T16:00:40Z

Jdn15:

File:JDN15ENDOTSV.gif

2018-03-07T15:46:37Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T15:37:03Z

Jdn15: /* Reaction Barrier and Reaction Energies */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Energy and Reaction Barrier Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CRXNV.gif]]
|[[File:JDN15CRXN2.LOG]]
[[File:JDN15CRXNP2.LOG]]
|}

===Reaction Energy and Reaction Barrier Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO DA'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO DA'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|-
|style="text-align: center;" |'''Cheletropic'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8
|}

File:JDN15ENDOTSEIGEN.LOG

2018-03-07T15:35:46Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T15:31:45Z

Jdn15: /* Reaction Energy Calculations */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Energy and Reaction Barrier Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CRXNV.gif]]
|[[File:JDN15CRXN2.LOG]]
[[File:JDN15CRXNP2.LOG]]
|}

===Reaction Barrier and Reaction Energies===

Rep:MOD:JDN15Y3lab

2018-03-07T15:28:15Z

Jdn15: /* Reaction Pathways */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Energy Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CRXNV.gif]]
|[[File:JDN15CRXN2.LOG]]
[[File:JDN15CRXNP2.LOG]]
|}

===Reaction Barrier and Reaction Energies===

Rep:MOD:JDN15Y3lab

2018-03-07T15:27:46Z

Jdn15: /* Reaction Pathways */

= Introduction =

=== Potential Energy Surface and Transition State ===
The Potential Energy Surface (PES) provides a graphical relationship between the energy of a molecule and its possible structures. The PES has 3N - 6 degree of freedom, where the minima refers to the chemically stable species (i.e. reactant and product) while the saddle point refers to the transition state. A transition state is the maximum point on the minimum energy path on a PES. By taking the second derivative at these points, we can differentiate between the reactants, products and transition state as the reactants and products will have a positive curvature in all coordinates while the transition state will have a negative curvature in only 1 coordinate. By utilising Gaussian software, a transition state can also be identified by having one imaginary (negative) frequency, while minima will have no imaginary frequencies.

=== Importance of studying Transition States ===
When one or more products can be formed, the transition states can be used to predict the product formed. For the formation of kinetic products, the pathway typically follows a lower activation energy and hence more stable transition state favoured.

=== Diels-Alder Reaction ===
Often referred to as a [4+2] cycloaddition, the Diels-Alder reaction typically occurs between an electron-rich diene and an electron-poor dienophile. This reaction is concerted and occurs via a single cyclic transition state to form a 6-membered ring.

Typically, the reaction occurs where the HOMO of the diene interacts with the LUMO of the dienophile.

In a hetero-Diels-Alder reaction, an inverse electron demand may occur (the diene is more electron-poor than the dienophile). As a result, the main orbitals interacting are the LUMO of the diene and the HOMO of the dienophile.

In reactions where there is a possibility of an endo and exo product in irreversible reactions, the kinetic endo product is preferred over the thermodynamic exo product. This is because the endo transition state is stabilised by orbital, dipolar and Van der Waals interactions between the dienophile and the diene, allowing the reaction to proceed at a faster rate. These stabilising interactions are absent in the exo transition state as the atoms on the dienophile and diene are too far away to interact. However, the exo product is the thermodynamic product due to less clashes in sterics.

In exercise 1, a simple Diels-Alder reaction between butadiene and ethylene was investigated. In exercise 2, a reaction between cyclohexadiene and 1,3-dioxole was investigated, where the formation of endo and exo adducts have to be further looked at. In exercise 3 involving xylylene and sulfur dioxide, a competing reaction known as Cheletropic reaction may occur.

=== Gaussview tool used for calculations ===
Gaussview software was used to analyse the transition structures and calculations were made to predict the reactivity of the reactions. The semi-empirical PM6 method and the Density Function Theory (DFT) B3LYP methods were employed to optimise the structures of the reactants, transition states and products. PM6 is a quicker method as it utilises experimental data to optimise the reaction structures, while B3LYP is more accurate but requires much more time.

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

=== Reaction Scheme ===
[[File:JDN15_Ex1.jpg|250px|centre]]

=== Molecular Orbitals ===
The reactants, cis-butadiene and ethene, as well as the product cyclohexene, and the transition state were optimised using PM6 method. The tables below show the Jmol files for the HOMO and LUMO of the reactants and the 4 MOs that are produced in the transition state (MO 16, MO17, MO18 and MO19). The transition state was then verified using an intrinsic reaction coordinate (IRC). [[File:JDN15TSIRC.LOG]]<br>
The HOMO of the electron-rich diene, ethene, and the LUMO of the electron poor dienophile, cis-butadine, interact in this conventional Diels-Alders reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene HOMO !! Butadiene LUMO !! Ethene HOMO !! Ethene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15BUTADIENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ETHYLENEJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! MO 16 !! MO 17 !! MO 18 !! MO 19
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>|| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:JDN15MO_EX1.png|400px|centre]]

[[File:JDN15MO1_TS.png|400px|centre]]The MO diagram for the transition state is drawn above (s for symmetric and a for anti-symmetric). Only orbitals with the same symmetry (i.e symmetric-symmetric, antisymmetric-antisymmetric) are able to interact as the orbital overlap integral is non-zero. When symmetric orbitals interact with anti-symmetric orbitals, the orbital integral is 0, therefore the overlap is forbidden.

=== Bond Length Analysis ===

{| class="wikitable" style="margin: 1em auto 1em auto;"
! Butadiene !! Ethene !! Transition State !! Cyclohexene
|-
|[[Image:JDN15Butadiene.png|100px]]
|[[Image:JDN15Ethene.png|100px]]
|[[Image:JDN15TS1.png|200px]]
|[[Image:JDN15Pdt1.png|200px]]
|}
Compared to the starting bonds, it is observed that there is a shortening of the bond length between C5 and C6, from 1.47 Å to 1.41 Å, suggesting a change from single bond to double bond. There is also a lengthening of bonds between C1-C6 and C4-C5, from 1.33 Å to 1.50 Å, suggesting a change from double bond to single bond.

The average sp<sup>3</sup> and sp<sup>2</sup> C-C bond lengths are 1.54 Å and 1.34 Å respectively. The Van der Waals radius of a C atom is 170 Å. In the transition state, the partially formed C-C bonds between C1-C2 and C3-C4 were 2.11 Å. This is longer than the average sp<sup>3</sup> but shorter than twice the Van der Waals radius of the C atom. This highlights that the orbitals are close enough to interact with each other but are not yet able to form a complete C-C bond.

=== Vibration of Reaction Path at Transition State ===
<jmol>
<jmolApplet>
<color>white</color>
<size>400</size>
<script>frame 7; vibration 1</script>
<uploadedFileContents>JDN15TSJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

The vibration corresponds to the reaction path at the transition state (-949.35cm<sup>-1</sup>). As ethene is a symmetric dienophile, both C have equal probability to become the electrophilic site. When the reactants are in the correct orientation and position, the formation of the 2 new sigma bonds happen rapidly hence the formation of the two bonds is synchronous.

==Exercise 2: Reaction of Cyclohexadiene and 1,3-dioxole==
===Reaction Scheme===
[[File:JDN15Ex2RXN.png|500px|centre]]

===Molecular Orbitals===
The reactants, cyclohexadiene and 1,3-dioxole, as well as the product and the transition state were calculated using PM6 method and optimised using B3LYP. The tables below show the Jmol files for the HOMO and LUMO of the reactants. Two sets of MOs are shown as well (MO 40, MO 41, MO 42, MO 43) for both exo and endo transition states.

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="3" |Reactants
|-
|
|style="text-align: center;"|'''HOMO'''
|style="text-align: center;"|'''LUMO'''
|-
|'''Cyclohexadiene'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8;mo 22; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 8; mo 23;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15CYCLOHEXADIENEDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''1,3-dioxole'''
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<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>JDN15DIOXOLEDFTJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
! colspan="6" |Transition States
|-
|
|style="text-align: center;" |'''Optimised'''
|style="text-align: center;"|'''MO 40'''
|style="text-align: center;"|'''MO 41''' (HOMO)
|style="text-align: center;"|'''MO 42''' (LUMO)
|style="text-align: center;"|'''MO 43'''
|-
|'''EXO'''
|<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>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|'''ENDO'''
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 40;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 41;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 42;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6; mo 43;mo nodots nomesh fill translucent; mo titleformat ""; zoom 0; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
A MO diagram was constructed from the energy levels of the MOs calculated above. 1,3-dioxole has 2 adjacent O which can donate electron density to the double bond, resulting in an electron-rich dienophile. This increase in electron density increases the energy of both the HOMO and LUMO of the dienophile, where the HOMO<sub>dienophile</sub> is higher than the HOMO<sub>diene</sub>. The HOMO<sub>dienophile</sub> is closer in energy to the LUMO<sub>diene</sub>, hence interacts stronger as compared to the HOMO<sub>diene</sub> interacting with the LUMO<sub>dienophile</sub>. This results in an inverse electron demand Diels-Alder reaction.
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Exo
!Endo
|-
|[[File:JDN15EX2MO.png |frameless|658x658px]]
|[[File:JDN15ENDO2MO.png|frameless|678x678px]]
|}

===Reaction Energy Calculations===
Reaction Energy = Energy of Product - Total Energy of Reactants
<br>
Reaction Barrier = Energy of TS - Total Energy of Reactants
<br>
{| class="wikitable" style="margin: 1em auto 1em auto;"
!Product
!Total Energy of Reactants (ha)
!Transition State (ha)
!Product (ha)
!Reaction Barriers (kJ / mol)
!Reaction Energies (kJ / mol)

|-
|style="text-align: center;" |'''EXO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3292
|style="text-align: center;" | -500.4173
|style="text-align: center;" | 166
|style="text-align: center;" |-65.1

|-
|style="text-align: center;" |'''ENDO'''
|style="text-align: center;" | -500.3925
|style="text-align: center;" | -500.3321
|style="text-align: center;" | -500.4187
|style="text-align: center;" | 158.6
|style="text-align: center;" |-68.8

|}

{| class="wikitable" style="margin: 1em auto 1em auto;"
|colspan="2" style="text-align: center;" | '''HOMO of Transition States'''
|-
!EXO
!ENDO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 12; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15EXOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>

|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>JDN15ENDOTSDJ.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

Typically, the exo product is the thermodynamically favoured product as the endo product is likely to have diaxial interactions. However, in this case, it is observed that both exo and endo products have steric clashes. From the table above, we observe that the reaction barrier for the formation of the endo product is lower than the formation of the exo product, suggesting that the endo product is more kinetically favourable. This is due to additional secondary (non-bonding) orbital interaction in the transition state, where the oxygen atoms on the 1,3-dioxole is able to interact with the cyclohexadiene, resulting in a lower transition state energy.<br>
The endo product is also the thermodynamic product, with a lower energy (more negative) than the exo-product. This is likely due to lesser steric clashes in the endo product compared to the exo product.

==Exercise 3: Diels-Alder vs Cheletropic==
===Reaction Scheme===
[[File:JDN15EX3RXN.png|600px|centre]]
As seen in the reaction Scheme, the reactants are able to react via 2 competing reactions, the Diels-Alder reaction and the Cheletropic reactions.

===Reaction Pathways===
The reactants, Xylylene and SO<sub>2</sub>, as well as the product and the transition state were optimised using PM6 method.
{| class="wikitable" style="margin: 1em auto 1em auto;"
! Xylylene !! SO<sub>2</sub>
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15XYLYLENE.LOG</uploadedFileContents>
</jmolApplet>
</jmol> || <jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 6</script>
<uploadedFileContents>JDN15SO2.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The tables below show the IRC for the EXO Diels-Alder reaction, ENDO Diels-Alder reaction and the Cheletropic reaction.

{| class="wikitable" style="margin: 1em auto 1em auto;"
!Reaction Pathway
!Visual Animation
!File Logs
|-
|'''EXO DA Reaction'''
|[[File:JDN15EXOTSV.gif]]
|[[File:JDN15EXOTSEIGEN.LOG]]
[[File:JDN15EXOPJ.LOG]]
|-
|'''ENDO DA Reaction'''
|[[File:JDN15ENDOTSV.gif]]
|[[File:JDN15ENDOTSEIGEN.LOG]]
[[File:JDN15ENDOPJ.LOG]]
|-
|'''Cheletropic Reaction'''
|[[File:JDN15CRXNV.gif]]
|[[File:JDN15CRXN2.LOG]]
[[File:JDN15CRXNP2.LOG]]

===Reaction Barrier and Reaction Energies===

File:JDN15ENDOPJ.LOG

2018-03-07T15:24:40Z

Jdn15:

File:JDN15EXOPJ.LOG

2018-03-07T15:19:58Z

Jdn15:

File:JDN15EXOTSEIGEN.LOG

2018-03-07T15:18:44Z

Jdn15:

File:JDN15EXOTSV.gif

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Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T14:46:58Z

Jdn15: /* Reaction Pathways */

Rep:MOD:JDN15Y3lab

2018-03-07T13:14:22Z

Jdn15: /* Reaction Pathways */

File:JDN15SO2.LOG

2018-03-07T13:13:00Z

Jdn15:

Rep:MOD:JDN15Y3lab

2018-03-07T13:11:09Z

Jdn15: /* Reaction Pathways */

File:JDN15XYLYLENE.LOG

2018-03-07T13:11:01Z

Jdn15: