ChemWiki - User contributions [en]

Rep:Mod:csw14TS

2017-01-27T11:51:38Z

Csw14: /* Reaction Profile */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

===Origin of Symmetry Requirements===
As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

===Bond Length Analysis===
The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

===Vibrational Analysis===
The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

===Reaction Profile===
The reaction profile of the cycloaddition can be seen below.

<center>
[[File:Rxncoord2csw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|Reactants
| -1.31x10<sup>6</sup>
|-
|E<sub>a, endo</sub>
|159.82
|-
|ΔG<sub>endo</sub>
|67.40
|-
|E<sub>a, exo</sub>
|167.64
|-
|ΔG<sub>exo</sub>
|63.81
|}
</center>

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there is an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

===Reaction Profile===
A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|590x590px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|83.43
|-
|ΔG<sub>endo</sub>
|97.37
|-
|E<sub>a, exo</sub>
|87.42
|-
|ΔG<sub>exo</sub>
|98.00
|-
|E<sub>a, cheletropic</sub>
|105.75
|-
|ΔG<sub>cheletropic</sub>
|154.33
|}
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

===Alternative Diels-Alder Reaction===
Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile and table of energy values below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making their formation thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

<center>
[[File:Extcoordcsw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|121.49
|-
|ΔG<sub>endo</sub>
|22.38
|-
|E<sub>a, exo</sub>
|113.65
|-
|ΔG<sub>exo</sub>
|17.92
|}
</center>

Rep:Mod:csw14TS

2017-01-27T11:48:41Z

Csw14: /* Exercise 2 */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

===Origin of Symmetry Requirements===
As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

===Bond Length Analysis===
The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

===Vibrational Analysis===
The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

===Reaction Profile===
The reaction profile of the cycloaddition can be seen below.

<center>
[[File:Rxncoord2csw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|Reactants
| -1.31x10<sup>6</sup>
|-
|E<sub>a, endo</sub>
|159.82
|-
|ΔG<sub>endo</sub>
|67.40
|-
|E<sub>a, exo</sub>
|167.64
|-
|ΔG<sub>exo</sub>
|63.81
|}
</center>

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

===Reaction Profile===
A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|590x590px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|83.43
|-
|ΔG<sub>endo</sub>
|97.37
|-
|E<sub>a, exo</sub>
|87.42
|-
|ΔG<sub>exo</sub>
|98.00
|-
|E<sub>a, cheletropic</sub>
|105.75
|-
|ΔG<sub>cheletropic</sub>
|154.33
|}
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

===Alternative Diels-Alder Reaction===
Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile and table of energy values below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making their formation thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

<center>
[[File:Extcoordcsw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|121.49
|-
|ΔG<sub>endo</sub>
|22.38
|-
|E<sub>a, exo</sub>
|113.65
|-
|ΔG<sub>exo</sub>
|17.92
|}
</center>

Rep:Mod:csw14TS

2017-01-27T11:42:50Z

Csw14: /* Exercise 2 */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

===Origin of Symmetry Requirements===
As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

===Bond Length Analysis===
The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

===Vibrational Analysis===
The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 16; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

===Reaction Profile===
The reaction profile of the cycloaddition can be seen below.

<center>
[[File:Rxncoord2csw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|Reactants
| -1.31x10<sup>6</sup>
|-
|E<sub>a, endo</sub>
|159.82
|-
|ΔG<sub>endo</sub>
|67.40
|-
|E<sub>a, exo</sub>
|167.64
|-
|ΔG<sub>exo</sub>
|63.81
|}
</center>

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

===Reaction Profile===
A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|590x590px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|83.43
|-
|ΔG<sub>endo</sub>
|97.37
|-
|E<sub>a, exo</sub>
|87.42
|-
|ΔG<sub>exo</sub>
|98.00
|-
|E<sub>a, cheletropic</sub>
|105.75
|-
|ΔG<sub>cheletropic</sub>
|154.33
|}
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

===Alternative Diels-Alder Reaction===
Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile and table of energy values below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making their formation thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

<center>
[[File:Extcoordcsw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|121.49
|-
|ΔG<sub>endo</sub>
|22.38
|-
|E<sub>a, exo</sub>
|113.65
|-
|ΔG<sub>exo</sub>
|17.92
|}
</center>

Rep:Mod:csw14TS

2017-01-27T11:39:18Z

Csw14: /* Exercise 2 */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

===Origin of Symmetry Requirements===
As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

===Bond Length Analysis===
The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

===Vibrational Analysis===
The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOMOscsw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

===Reaction Profile===
The reaction profile of the cycloaddition can be seen below.

<center>
[[File:Rxncoord2csw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|Reactants
| -1.31x10<sup>6</sup>
|-
|E<sub>a, endo</sub>
|159.82
|-
|ΔG<sub>endo</sub>
|67.40
|-
|E<sub>a, exo</sub>
|167.64
|-
|ΔG<sub>exo</sub>
|63.81
|}
</center>

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

===Reaction Profile===
A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|590x590px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|83.43
|-
|ΔG<sub>endo</sub>
|97.37
|-
|E<sub>a, exo</sub>
|87.42
|-
|ΔG<sub>exo</sub>
|98.00
|-
|E<sub>a, cheletropic</sub>
|105.75
|-
|ΔG<sub>cheletropic</sub>
|154.33
|}
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

===Alternative Diels-Alder Reaction===
Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile and table of energy values below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making their formation thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

<center>
[[File:Extcoordcsw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|121.49
|-
|ΔG<sub>endo</sub>
|22.38
|-
|E<sub>a, exo</sub>
|113.65
|-
|ΔG<sub>exo</sub>
|17.92
|}
</center>

File:RXN2EXOMOscsw14.log

2017-01-27T11:37:40Z

Csw14:

File:RXN2ENDOMOscsw14.log

2017-01-27T11:37:16Z

Csw14:

File:RXN2MOscsw14.log

2017-01-27T11:36:24Z

Csw14:

Rep:Mod:csw14TS

2017-01-27T11:30:18Z

Csw14: /* Exercise 2 */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

===Origin of Symmetry Requirements===
As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

===Bond Length Analysis===
The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

===Vibrational Analysis===
The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 40; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOB3LYP3csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 41; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOB3LYP3csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 42; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOB3LYP3csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 2; mo 43; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOB3LYP3csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

===Reaction Profile===
The reaction profile of the cycloaddition can be seen below.

<center>
[[File:Rxncoord2csw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|Reactants
| -1.31x10<sup>6</sup>
|-
|E<sub>a, endo</sub>
|159.82
|-
|ΔG<sub>endo</sub>
|67.40
|-
|E<sub>a, exo</sub>
|167.64
|-
|ΔG<sub>exo</sub>
|63.81
|}
</center>

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

===Reaction Profile===
A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|590x590px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|83.43
|-
|ΔG<sub>endo</sub>
|97.37
|-
|E<sub>a, exo</sub>
|87.42
|-
|ΔG<sub>exo</sub>
|98.00
|-
|E<sub>a, cheletropic</sub>
|105.75
|-
|ΔG<sub>cheletropic</sub>
|154.33
|}
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

===Alternative Diels-Alder Reaction===
Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile and table of energy values below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making their formation thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

<center>
[[File:Extcoordcsw14.png|540x540px]]
{| class="wikitable"
!Energy gap
!Energy (kJ/mol)
|-
|E<sub>a, endo</sub>
|121.49
|-
|ΔG<sub>endo</sub>
|22.38
|-
|E<sub>a, exo</sub>
|113.65
|-
|ΔG<sub>exo</sub>
|17.92
|}
</center>

Rep:Mod:csw14TS

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

The reaction profile of the cycloaddition can be seen below.

'''INSERT REACTION PROFILE'''

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

<center>
[[File:Rxncoord3csw14.png|440x440px]]
</center>

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making them thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

'''INSERT REACTION PROFILE'''

File:Rxncoord3csw14.png

2017-01-27T09:45:02Z

Csw14:

Rep:Mod:csw14TS

2017-01-27T09:26:53Z

Csw14: /* Exercise 2 */

== Introduction ==
In this lab, the Gaussian program was used to identify transition states and minima on the potential energy surface of pericyclic reactions. The pericyclic reactions investigated were the [4+2]-cycloaddition, also known as the Diels-Alder reaction, and the cheletropic reaction.

The potential energy surface (PES) is a function that shows the overall energy of the molecule with respect to its configuration. Minima on the PES correspond to favourable, stable configurations of the systems. Generally, there are many local minima on the potential energy surface. However, when perturbed, the system can be optimized further to find the global minimum, or the most stable configuration of the system. Conversely, transition states are high energy configurations that the system can adopt. They appear as maxima on the PES. The molecule corresponding to the transition state is often a transient contorted species.

The gradient at both the minima and transition states is zero with respect to the PES. However, the curvature, or the second derivate of the PES, is different at the two types of points. If the curvature is positive, the point is a minimum. If it is negative, the point is a transition state. The curvature of the PES also relates to the vibrational frequencies of the molecules - thus, transition state structures have a negative frequency.

All structures were initially optimized to the PM6 level. This allowed for faster calculations as this method does not require an atomic basis set to be defined; instead, it relies on empirical data to guess the structures. The structures in exercise 2 were further optimized to the B3LYP/6-31G(d) level. This method uses the density functional theory and gives more rigorous outputs. It is, as a result, more computationally intensive.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting.

The HOMO and LUMO MOs of butadiene and ethene are shown below.
<center>
{| class="wikitable"
!Butadiene
!Ethene
|-
|<jmol>
<jmolApplet>
<title>LUMO (MO 12)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 12; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 7)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 7; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|<jmol>
<jmolApplet>
<title>HOMO (MO 11)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 11; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>Csw14BUTADIENE_OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 6)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 6; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>ETHENEOPTcsw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 16, MO 17, MO 18, and MO 19 in the Gaussian computation. They are shown below.
<center>
{| class="wikitable"
!Transition state
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 16)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 16; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 17)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 17; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 18)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 18; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 19)</title>
<color>white</color>
<size>300</size>
<script>frame 12; mo 19; mo dots nomesh fill translucent; mo titleformat ""; rotate x 90; rotate y 90</script>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

It can be seen from the transition state MOs that the orbitals are combinations of reactant frontier orbitals with the same symmetry. MOs ψ1 and ψ2 were formed from butadiene and ethene orbitals of the same phase, resulting in regions of increased electron density, or bonding interactions, in the transition state. On the other hand, MOs ψ3 and ψ4 were formed from orbitals of different phases, resulting in nodes, or anti-bonding interactions, in the transition state.

As stated earlier, symmetric and asymmetric frontier orbitals do not combine with each other, but only with other orbitals of the same symmetry. This symmetry requirement for the formation of molecular orbitals arises from quantum mechanics. The overlap integral S<sub>AB</sub> gives the extent of interaction between two orbitals, A and B. It involves the product of a wavefunction and a complex conjugate.
<center><math>\mathbf{S}_\mathrm{AB}=\int \Psi_\mathrm{A}^* \Psi_\mathrm{B} \, dV</math></center>
If both terms in the integral are symmetric or asymmetric, the product will be symmetric and give a non-zero integral. However, if one is symmetric and one is asymmetric, the product will be asymmetric and its integral will be zero. The overlap integral S<sub>AB</sub> would thus also be zero, indicating that there is no interaction between the orbitals.

The C-C bond lengths of butadiene, ethene, and cyclohexene are shown below. The bond lengths are in agreement with typical carbon bond lengths for the respective hybridization modes.
<center>
{| class="wikitable"
!Butadiene
!Ethene
!Cyclohexene
|-
|[[File:Butadienecsw14.png|449x449px]]
|[[File:Ethenecsw14.png|350x350px]]
|[[File:Product1csw14.png|304x304px]]
|}
</center>

<center>
{| class="wikitable"
!Type of Bond
!Typical length (Å)
|-
|sp<sup>3 </sup>'''C '''- sp<sup>3 </sup>'''C'''
|1.54
|-
|sp<sup>3 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.50
|-
|sp<sup>2 </sup>'''C''' - sp<sup>2 </sup>'''C'''
|1.34
|-
|'''C''' Van der Waals radius
|1.70
|}
</center>

The C-C bond lengths in the transition state are shown below. The bond lengths of the starting materials have become intermediates between C-C single and double bonds. The bond length of the ethene fragment has shortened; the terminal C-C bonds of the butadiene molecule have lengthened and the central bond has shortened. This indicates that electron density is shifting to break the existing pi bonds and form new pi and sigma bonds. The distance between the terminal carbons of the butadiene and the carbons are ethene are less than 2 times the Van der Waals radius of carbon, indicating that bonding interactions are forming between the two fragments.
<center>
{| class="wikitable"
!Transition State
|-
|[[File:TS1csw14.png|303x303px]]
|}
</center>

The vibration of the transition state that corresponds to the reaction path is shown below. The vibration has a negative frequency; because it occurs at a maximum on the potential energy surface, where the curvature is negative, the vibration is also negative. Based on the vibration, it can be seen that the formation of the two new bonds is a synchronous process.

<center>
{| class="wikitable"
!Transition State Vibration
|-
|<jmol><jmolApplet>
<color>white</color>
<size>300</size>
<uploadedFileContents>RXN1TSPM6csw14.LOG</uploadedFileContents>
<script>frame 13; vibration 2</script>
</jmolApplet></jmol>
|}
</center>

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO and LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

The new transition state MOs for both the endo and exo product can be seen below. The transition state MOs ψ1, ψ2, ψ3, and ψ4 correspond to MO 40, MO 41, MO 42, and MO 43 for both the endo and exo pathways in the Gaussian computation.

<center>
{| class="wikitable"
!Endo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40) </title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 10; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
!Exo
|<jmol>
<jmolApplet>
<title>HOMO - 1 (MO 40)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 29; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>HOMO (MO 41)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO (MO 42)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 32; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<title>LUMO + 1 (MO 43)</title>
<color>white</color>
<size>300</size>
<script>frame 42; mo 31; mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

The HOMO and LUMO of the transition state are both symmetric, indicating that they were formed from symmetric frontier orbitals. The dienophile HOMO and the diene LUMO are symmetric, indicating that they indeed formed the HOMO and LUMO of the transition state. Additionally, the HOMO-1 and LUMO+1 pair are both anti-symmetric, indicating that they were formed from the asymmetric dienophile LUMO and diene HOMO. Thus, the reaction is an example of an inverse electron demand Diels-Alder reaction.

The reaction profile of the cycloaddition can be seen below.

'''INSERT REACTION PROFILE'''

The endo product is both kinetically and thermodynamically favoured over the exo product. Though it appears be more sterically hindered and thus unstable, the endo transition state may instead be stabilized by secondary orbital interactions, lowering the activation energy barrier. In the HOMOs of the two transition states shown below, it can be seen that there may be an interaction between the oxygens of the dienophile and the central carbons of the diene in the endo transition state. The region around the oxygens is out of phase with the rest of the electron density surrounding the dienophile but in phase with the diene; the stabilization provided by the central carbons of the diene may thus have a significant effect in the overall lowering of the transition state energy. This interaction is absent in the exo transition state.

<center>
{| class="wikitable"
!Endo TS HOMO
!Exo TS HOMO
|-
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 10; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2ENDOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|<jmol>
<jmolApplet>
<color>white</color>
<size>300</size>
<script>frame 42; mo 30; mo cutoff 0.01;mo dots nomesh fill translucent; mo titleformat ""</script>
<uploadedFileContents>RXN2EXOPM6csw14.log</uploadedFileContents>
</jmolApplet>
</jmol>
|}
</center>

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

'''INSERT REACTION PROFILE'''

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making them thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

'''INSERT REACTION PROFILE'''

2017-01-27T09:02:10Z

Csw14: /* Introduction */

Rep:Mod:csw14TS

2017-01-27T08:41:15Z

Csw14: /* Exercise 3 */

== Introduction ==
Minima on the potential energy surface correspond to favourable, stable configurations for the system. However, there are many local minima on the potential energy surface that can lead to lower energy configurations.
Transition states appear as maxima on the potential energy surface. They are transient, high-energy species that exist on lowest energy reaction pathways.
The gradient at both minima and transition states is zero. The curvature at a minimum is positive; the curvature at a transition state is negative.

== Exercise 1 ==
In this exercise, the [4+2]-cycloaddition of butadiene and ethene is modelled. The overall reaction involves the dissociation of 2 pi bonds and formation of 2 sigma bonds. The MO diagram of the frontier orbitals of butadiene and ethene and the orbitals of the transition state can be seen below.

[[File:Rxn1 MOscsw14.png|center|630x630px]]

As seen in the diagram, the HOMO and LUMO orbitals of the butadiene and ethene combine to form 4 new transition state MOs. The butadiene and ethene orbitals of the same symmetry combine; the asymmetric butadiene HOMO combines with the asymmetric ethene LUMO while the symmetric butadiene LUMO combines with the symmetric ethene HOMO. As the butadiene LUMO and the ethene HOMO are closer in energy and thus have a larger interaction, the resulting transition state MOs have a larger splitting. The HOMO and LUMO of the transition state, however, are formed by the butadiene HOMO and the ethene LUMO; thus, the cycloaddition between butadiene and ethene can be considered a normal electron demand Diels-Alder reaction.

== Exercise 2 ==
In this exercise, the [4+2]-cycloaddition between cyclohexadiene and 1,3-dioxole is modelled. There are two possible products that can be formed - the endo product and the exo product. The endo product is formed via a transition state where the cyclohexadiene and 1,3-dioxole molecules are overlapping. The exo product is formed via a transition state where the 1,3-dioxole molecule is pointing away from the cyclohexadiene.

The MO diagram of the frontier orbitals of cyclohexadiene and 1,3-dioxole and the orbitals of the transition state can be seen below. While the transition state in the MO diagram shows the overlap that will give the endo product, the frontier orbital interactions and relative energies of the transition state MOs are identical for the transition state of the exo product.

[[File:Rxn2_MOscsw14.png|centre|630x630px]]

The reaction between cyclohexadiene and 1,3-dioxole is an example of an inverse electron demand Diels-Alder reaction. As the dienophile has electron-donating -OR substituents, the energies of its HOMO & LUMO increase. In this scenario, the interaction between the dienophile HOMO and diene LUMO form the HOMO and LUMO of the transition state.

== Exercise 3 ==
In this exercise, the [4+2]-cycloaddition between ortho-xylylene and sulphur dioxide is modelled. Like the reaction in exercise 2, the cycloaddition can result in an endo or an exo product. The subtrates can also undergo a cheletropic reaction, giving a total of three possible products for the reaction between ortho-xylylene and sulphur dioxide.

Like the Diels-Alder reaction, the cheletropic reaction is also a pericyclic reaction. It involves the formation of 2 new bonds to the same atom on one of the reactants. In this case, the xylylene forms 2 new bonds to the sulphur of SO<sub>2</sub>.

The reaction coordinates of the endo Diels-Alder, exo Diels-Alder, and cheletropic reactions can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
!Cheletropic
|-
|[[File:EndoIRCcsw14.gif|400x400px]]
|[[File:ExoIRCcsw14.gif|400x400px]]
|[[File:csw14CheletropicIRC.gif|400x400px]]
|}
</center>

It can be seen that bond formation is asynchronous in the Diels-Alder reactions. This may be attributed to the fact that the dienophile is composed of two different heteroatoms. The bond formation is synchronous, however, in the cheletropic reaction as both new bonds are formed with the same heteroatom. It can also be seen that the 6-membered ring of xylylene gains aromaticity over the course of all three reactions. The drive to form an aromatic product may explain the enhanced reactivity of xylylene.

A reaction profile with the relative energies of the reactants, transition states, and products can is shown below.

'''INSERT REACTION PROFILE'''

The endo product is the kinetic product for this reaction. Once again, the transition state is most likely stabilized by secondary orbital interactions between the oxygen on SO<sub>2</sub> and the diene. The cheletropic product is the thermodynamic product for this reaction.

Xylylene has a second diene fragment that can undergo the Diels-Alder reaction with SO<sub>2</sub> to give an endo or an exo product.

<center>
[[File:Extrxnschemecsw14.png|440x440px]]
</center>

The reaction coordinates of the endo and exo Diels-Alder reactions at this site can be seen below.

<center>
{| class="wikitable"
!Endo
!Exo
|-
|[[File:ExtexoIRCcsw14.gif|400x400px]]
|[[File:ExtendoIRCcsw14.gif|400x400px]]
|}
</center>

While the reaction is possible, it is both thermodynamically and kinetically unfavourable. As seen in the reaction profile below, the activation energies for both the endo and exo reactions are very high, making them kinetically unfavourable. Additionally, the energies of the products are higher than that of the reactants, making them thermodynamically unfavourable. A contributing factor may be that the product does not attain aromaticity like those of the previous reaction.

'''INSERT REACTION PROFILE'''