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Rep:Mod:ts exercise sp3815

2017-11-08T11:21:16Z

Sp3815: /* Conclusion */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is an intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

<jmol><jmolApplet>
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<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

{| class="wikitable"
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favoured product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/6-31G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO<sub>2</sub> show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T11:20:08Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
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! <jmol><jmolApplet>
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====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is an intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

<jmol><jmolApplet>
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<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favoured product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/631-G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO<sub>2</sub> show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T11:13:27Z

Sp3815: /* Bond Distances */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is an intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favourable product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/631-G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO<sub>2</sub> show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T11:09:03Z

Sp3815: /* Introduction */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favourable product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/631-G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO<sub>2</sub> show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T11:03:02Z

Sp3815: /* Conclusion */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favourable product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/631-G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

In the reaction between butadiene and ethylene, the MO diagram shows that only MOs with the same symmetry interact and the vibration corresponding to the reaction pathway shows that the two new σ bonds are formed synchronously. The MO diagram for the reaction between cyclohexadiene and 1,3-dioxole shows that the reaction is an inverse demand Diels Alder and the thermochemistry results show that the endo product is both the kinetically and thermodynamically favoured product. The IRC calculations for the reaction between xylylene and SO<sub>2</sub> show that the six membered ring is aromatised in all three reactions and the thermochemistry results show that the Diels Alder endo product is the kinetic product and the cheletropic product is the thermodynamic product.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T10:48:46Z

Sp3815: /* Conclusion */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favourable product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===
In this computational laboratory, Gaussian was used to optimise reactants, products and transition state structures at a PM6 and B3LYP/631-G(d) levels. Results from these optimisations show the energies and visualisations of MOs involved in the reaction, how the bond distances change through the reaction and the thermodynamic data for the reaction. IRC calculations of the transition states were also used to verify that the transition structure was correct and that the reaction proceeds as expected.

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T10:28:57Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The free energy of the cheletropic product is 56.97 KJmol<sup>-1</sup> lower than the endo product. The free energy of the cheletropic product is also 56.32 KJmol<sup>-1</sup> lower than the exo product. The cheletropic product is the most thermodynamically stable product and is therefore the thermodynamically favourable product which is formed under equilibrating conditions.

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T10:12:59Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
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<title>Antisymmetric Anti-Bonding MO</title>
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====Bond Distances====

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! <jmol><jmolApplet>
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<title>C-C Bond Lengths in Cyclohexene</title>
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<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
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<title>Endo Asymmetrical Anti Bonding MO</title>
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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

{| class="wikitable"
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The Diels Alder endo reaction barrier is 3.89 KJmol<sup>-1</sup> lower than the exo reaction barrier. The endo reaction barrier is also 22.30 KJmol<sup>-1</sup> lower in energy than the cheletropic product. The endo product has the lowest activation energy and hence has the fastest rate of formation. The endo product has the greatest rate of formation as there are favourable bonding interactions between the S=O of SO<sub>2</sub> and the forming π bond in the transition state. This favourable interaction decreases the free energy of the transition state and therefore the activation barrier. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:59:34Z

Sp3815: /* IRC */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consists of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The transformation of the highly unstable xylylene to the highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:55:05Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

<jmol><jmolApplet>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more thermodynamically stable than the exo product, therefore the endo product is also the thermodynamically favoured product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state for the exo product. The steric hindrance increases the energy of the transition state which increases the activation energy and hence decreases the rate of formation of the exo product. Furthermore the steric hindrance destabilises the final product resulting in the exo product having a higher free energy.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:48:20Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction, the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap which results in the greatest orbital interaction is between the HOMO of the diene and the LUMO of the dienophile. In the inverse demand Diels Alder reaction, the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap which results in the greatest orbital interaction is between the HOMO of the dienophile and the LUMO of the diene.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:34:20Z

Sp3815: /* Vibrations in the Transition State */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous as the two terminal carbon atoms of the butadiene and the two carbon atoms of the ethylene are approaching each other at the same time.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:31:56Z

Sp3815: /* Bond Distances */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate length between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other in the correct orientation to eventually form the C-C single bonds.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
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<script>frame 1.30</script>
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:27:45Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is smaller than the HOMO-LUMO gap than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden and therefore the orbital overlap integral is zero. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
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<title>Symmetric Anti-Bonding MO</title>
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====Bond Distances====

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<title>C-C Bond Distance in Ethylene</title>
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! <jmol><jmolApplet>
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<title>C-C Bond Lengths in Cyclohexene</title>
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<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
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<title>Endo Asymmetrical Anti Bonding MO</title>
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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:12:46Z

Sp3815: /* Bibliography */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.

2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.

3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T09:12:18Z

Sp3815: /* Transition States and Reactivity */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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! <jmol><jmolApplet>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

===Conclusion===

===Bibliography===
1. Wales DJ. ''Energy Landscapes: Applications to Clusters, Biomolecules and Glasses''. Cambridge: Cambridge University Press;2003. p 1-5.
2. Clayden J, Greeves N, Warren S. ''Organic Chemistry''.2<sup>nd</sup> Edition. Oxford: Oxford University Press; 2001. p.141-148.
3. Batsanov SS. Van der Waals Radii of Elements. ''Inorganic Materials''. 2001; 37(9): 871–885. Available from:https://doi.org/10.1023/A:1011625728803

Rep:Mod:ts exercise sp3815

2017-11-08T08:39:11Z

Sp3815: /* IRC */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|frame|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|frame|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|frame|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-08T08:32:48Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.

In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder reaction.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-08T08:31:49Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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In a normal demand Diels Alder reaction. the diene which is electron rich has higher energy molecular orbitals than the dienophile which is electron poor. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO energy gap is between the HOMO of the diene and the LUMO of the dienophile which results in the greatest interaction. In the inverse demand Diels Alder reaction. the diene has lower energy molecular orbitals than the dienophile. Therefore in the frontier orbital diagram, the smallest HOMO-LUMO gap is between the HOMO of the dienophile and the LUMO of the diene which results in the greatest interactions.
In both the endo and exo Diels Alder reaction between cyclohexadiene and 1,3-dioxole, the HOMO of cyclohexadiene is 25.28 KJmol<sup>-1</sup> lower in energy than the HOMO of 1,3-dioxole. Furthermore the LUMO of cyclohexadiene is 144.61 KJmol<sup>-1</sup> lower in energy than the LUMO of 1,3-dioxole. The molecular orbitals of the 1,3-dioxole dienophile have a greater energy than the cyclohexadiene molecular orbitals. The ether groups of the 1,3-dioxole are electron donating groups due to the lone pair of electrons in the p orbital of the ether oxygen, the presence of these electron donating groups increases the energy of the dienophile molecular orbitals. The HOMO-LUMO energy gap for the HOMO of the diene and the LUMO of the dienophile as for a normal demand Diels Alder is 639.36 KJmol<sup>-1</sup> and the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene as for an inverse demand Diels Alder is 469.47 KJmol<sup>-1</sup>. Therefore as the HOMO-LUMO energy gap for the HOMO of the dienophile and the LUMO of the diene is the smallest, the Diels Alder reaction between cyclohexadiene and 1,3-dioxole is an inverse demand Diels Alder.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-07T22:49:06Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM_2.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

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[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

File:SP3815 ENDO FINAL MO DIAGRAM 2.jpg

2017-11-07T22:48:34Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-07T22:44:38Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
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<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
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<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
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<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_ENDO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
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<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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|}

[[File:SP3815_EXO_FINAL_MO_DIAGRAM.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
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<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Endo TS</title>
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<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 8 Secondary Interactions in the HOMO of Exo TS</title>
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<size>300</size>
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

File:SP3815 EXO FINAL MO DIAGRAM.jpg

2017-11-07T22:44:20Z

Sp3815:

File:SP3815 ENDO FINAL MO DIAGRAM.jpg

2017-11-07T22:43:23Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-07T22:29:42Z

Sp3815: /* Reaction */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which a six membered ring product is formed through the formation of two new sigma bonds.

[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
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<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
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<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
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<title>LUMO of Ethylene</title>
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{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
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<title>Antisymmetric Anti-Bonding MO</title>
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====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 8 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-07T22:27:28Z

Sp3815: /* Reaction */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|400px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
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|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Exo Symmetric Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
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<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Figure 7 Secondary Interactions in the HOMO of Endo TS</title>
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<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 8 Secondary Interactions in the HOMO of Exo TS</title>
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<size>300</size>
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|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-07T22:27:11Z

Sp3815: /* Transition States and Reactivity */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State in the Reaction between Butadiene and Ethylene]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
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! <jmol><jmolApplet>
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<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
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{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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<title>Symmetric Bonding MO</title>
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<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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<title>Symmetric Anti-Bonding MO</title>
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<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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<title>Antisymmetric Anti-Bonding MO</title>
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====Bond Distances====

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! <jmol><jmolApplet>
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<title>C-C Bond Distances in Butadiene</title>
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! <jmol><jmolApplet>
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<title>C-C Bond Distance in Ethylene</title>
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<script>frame 1.14;measure 1 4</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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<title>C-C Bond Lengths in Transition State</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
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<title>C-C Bond Lengths in Cyclohexene</title>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration of the Transition State corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Endo Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Endo Symmetrical Anti Bonding MO</title>
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! <jmol><jmolApplet>
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[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 6 Molecular Orbital Diagram for the Formation of the Exo Transition State]]

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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 7 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 8 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
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<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 9 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 10''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 11''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 12''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 10, 11 and 12, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 13 Reaction Profile for the three possible reactions between Xylylene and SO<sub>2</sub>]]

Rep:Mod:ts exercise sp3815

2017-11-07T22:09:09Z

Sp3815: /* Reaction Profile */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|750px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

Rep:Mod:ts exercise sp3815

2017-11-07T22:08:26Z

Sp3815: /* Reaction Profile */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
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{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
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<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
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|}

====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
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<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
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! <jmol><jmolApplet>
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<title>C-C Bond Distance in Ethylene</title>
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
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<title>C-C Bond Lengths in Cyclohexene</title>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
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</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
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<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====
[[File:SP3815_Q3_REACTION_PROFILE.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

File:SP3815 Q3 REACTION PROFILE.jpg

2017-11-07T22:04:23Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-07T21:10:29Z

Sp3815: /* Bond Distances */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
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{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
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<size>200</size>
<script>frame 1.14;measure 1 4</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
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<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
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|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
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<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Endo Symmetrical Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Endo Asymmetrical Anti Bonding MO</title>
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</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Exo Symmetric Anti Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
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====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
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<size>300</size>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T21:09:51Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
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<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
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! <jmol><jmolApplet>
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<title>Antisymmetric Anti-Bonding MO</title>
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<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
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====Bond Distances====

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! <jmol><jmolApplet>
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<title>C-C Bond Distances in Butadiene</title>
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! <jmol><jmolApplet>
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<title>C-C Bond Distance in Ethylene</title>
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Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
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<script>frame 1.23;vibration 1</script>
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The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
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<title>Endo Symmetrical Anti Bonding MO</title>
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! <jmol><jmolApplet>
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[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

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====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T21:09:22Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

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====Bond Distances====

{| class="wikitable"
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<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T21:07:29Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
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<title>Exo Symmetric Anti Bonding MO</title>
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

File:SP3815 MO DIAGRAM CD.jpg

2017-11-07T21:07:04Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-07T19:55:34Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T19:53:07Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
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<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
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<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
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! <jmol><jmolApplet>
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<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
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{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
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<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
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|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
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<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
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<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
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<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
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|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CD_FINAL.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
[[File:SP3815_MO_DIAGRAM_CD_FINAL_EXO.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
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<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
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<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
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<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
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<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
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<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
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|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
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<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
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</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
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===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

File:SP3815 MO DIAGRAM CD FINAL EXO.jpg

2017-11-07T19:52:12Z

Sp3815:

File:SP3815 MO DIAGRAM CD FINAL.jpg

2017-11-07T19:51:34Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-07T15:18:02Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
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{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
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<title>Asymmetric Bonding MO</title>
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
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! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
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<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
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|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
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<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
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! <jmol><jmolApplet>
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! <jmol><jmolApplet>
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<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_Q2_MO_DIAGRAM_CORR.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T15:14:44Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_Q2_MO_DIAGRAM_CORR.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| border="1" cellpadding="5" cellspacing="0" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T15:12:18Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_Q2_MO_DIAGRAM_CORR.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable" align="center"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-07T10:46:49Z

Sp3815: /* Molecular Orbital Diagram */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_Q2_MO_DIAGRAM_CORR.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

File:SP3815 Q2 MO DIAGRAM CORR.jpg

2017-11-07T10:45:23Z

Sp3815:

Rep:Mod:ts exercise sp3815

2017-11-06T21:38:15Z

Sp3815: /* IRC */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

In all the reactions shown in figure 9, 10 and 11, initially the bonding in the six membered ring consisted of a conjugated diene, however, as the reaction proceeds, the six membered ring becomes aromatised to a benzene ring. The formation of this highly stabilised benzene ring is a driving force for all three reactions.

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-06T21:20:56Z

Sp3815: /* IRC */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-06T21:17:26Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product. The Cheletropic product has the lowest free energy because there is no steric hindrance...

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-06T20:31:23Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. In the endo product transition state there is favourable bonding interactions between the S=O group and the forming π bond which decreases the energy of the transition state and therefore decreases the activation energy.

The Cheletropic product has the lowest free energy compared to the endo and exo Diels Alder products and is therefore the thermodynamically favoured product.

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-06T20:12:22Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

The reaction barrier for the formation of the endo Diels Alder product is lower in energy than both the exo Diels Alder product and the Cheletropic product, therefore the endo product has the highest rate of formation. The endo product is the kinetically favoured product and is formed at room temperature under non-equilibrating conditions. The endo

====Reaction Profile====

Rep:Mod:ts exercise sp3815

2017-11-06T19:51:24Z

Sp3815: /* Thermochemistry */

==Transition States and Reactivity==
===Introduction===
Wales(1) states that a potential energy surface represents the potential energy of a given system as a function of all the relevant atomic and molecular co-ordinates which is also known as the reaction co-ordinate. Minima on the potential energy surface usually correspond to reactants, products or intermediates of the reaction. At the minima, the gradient is equal to zero and the second derivative is greater than zero. The maxima on potential energy surfaces correspond to transition states. At the maxima, the gradient is also equal to zero, however, the second derivative is less than zero. The system spends the majority of the time at the minima, however, fluctuations in the energy of the system may result in the system reaching the transition state maxima, at the maxima, the system is either reflected back to the original minimum or proceeds to the next minimum.

===Exercise 1: Reaction of Butadiene with Ethylene===
====Reaction====
The [4+2]-cycloaddition reaction between s-cis-butadiene and ethylene proceeds through a concerted mechanism in which two new sigma bonds are formed resulting in a six membered ring product.
[[File:SP3815 Q1 MECHANISM.jpg|center|500px|thumb|Figure 1 Mechanism for the reaction between butadiene and ethylene]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_DIAGRAM_CORRECTED.jpg|centre|600px|thumb|Figure 2 Molecular Orbital Diagram for the Formation of the Transition State]]

Figure 2 shows the molecular orbital diagram for the formation of the transition state in the reaction between butadiene and ethylene. The energies of the butadiene and ethylene MOs are determined by the number of nodes. The HOMO of both ethylene and butadiene have one node and the LUMO of ethylene and butadiene have two nodes so are higher in energy. Due to the increased conjugation in butadiene, the HOMO-LUMO gap in butadiene is greater than ethylene. The [4+2]-cycloaddition between butadiene and ethylene occurs due to HOMO-LUMO interactions. The energy gap between the HOMO of butadiene and the LUMO of ethylene is similar to the energy gap between the LUMO of butadiene and the HOMO of ethylene and therefore both of these interactions results in a similar splitting of energies in the resulting MOs in the transition state.

The MO diagram shows that only MOs with the same symmetry will interact to form MOs in the transition state. Symmetric-Symmetric and Asymmetric-Asymmetric interactions are allowed and therefore have a non-zero orbital overlap integral. Symmetric-Asymmetric interactions are forbidden. When the symmetry of the interacting MOs are different then the constructive overlap of orbitals is completely cancelled by the same extent of destructive overlap.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>HOMO of Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76; mo 11; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>
! <jmol><jmolApplet>
<title>LUMO of Butadiene</title>
<color>white</color>
<size>200</size>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<script>frame 1.76; mo 12; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>HOMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 6; mo nodots mesh fill translucent; mo titleformat "";</script></jmolApplet></jmol>

! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>LUMO of Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14; mo 7; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 16; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 17; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Symmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 18; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>Antisymmetric Anti-Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;mo 19; mo nodots mesh fill translucent; mo titleformat "";</script>
</jmolApplet></jmol>
|}

====Bond Distances====

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_BUTADIENE_OPT_PM62.LOG</uploadedFileContents>
<script>frame 1.76</script>
<title>C-C Bond Distances in Butadiene</title>
<color>white</color>
<size>200</size>
<script>frame 1.76;measure 1 4;measure 4 6;measure 6 7</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ETHENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.14</script>
<title>C-C Bond Distance in Ethylene</title>
<color>white</color>
<size>200</size>
<script>frame 1.14;measure 1 4</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.22</script>
<title>C-C Bond Lengths in Transition State</title>
<color>white</color>
<size>200</size>
<script>frame 1.22;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_CYCLOHEXENE_OPT_PM6.LOG</uploadedFileContents>
<script>frame 1.12</script>
<title>C-C Bond Lengths in Cyclohexene</title>
<color>white</color>
<size>200</size>
<script>frame 1.12;measure 1 4;measure 4 6;measure 6 7;measure 7 14;measure 14 11
;measure 11 1</script>
</jmolApplet></jmol>
|}

Clayden(2) et al states that a typical C-C single bond length is around 0.154 nm and a typical C=C double bond is 0.133 nm. However, the C-C single bond in butadiene has double bond character and therefore has a shorter length of 0.147 nm due to the conjugation of the two C=C double bonds. The C=C bond lengths in butadiene and ethylene are 0.133 nm which matches the typical sp<sup>2</sup> C=C bond length. During the reaction, the C-C single bond length in butadiene decreases changing to a C=C double bond of length 0.134 nm in the product. The two C=C double bond lengths in butadiene increase to form two C-C single bonds of length 0.150 nm in the product. Furthermore, the C=C double bond length in ethylene increases to form a C-C single bond of length 0.154 nm. The new C-C single bonds which form in the reaction match the typical sp<sup>3</sup> C-C single bond length. It is energetically favourable to convert two π bonds to two σ sigma bonds and this is the driving force for this reaction.

Batsanov(3) states that the van der Waals radius of carbon is 0.17 nm and therefore the van der Waals diameter is equal to 0.34 nm. In the transition state the bonds forming between the butadiene and ethylene have a length of 0.211 nm which is intermediate between the van der Waals diameter and the typical sp<sup>3</sup> C-C single bond length. This shows that in the transition state the C-C single bonds have not formed yet, however, the butadiene and ethylene molecules are approaching each other.

====Vibrations in the Transition State====

<jmol><jmolApplet>
<uploadedFileContents>SP3815_Q1_TS_OPT_PM6.LOG</uploadedFileContents>
<title>Figure 3 Vibration corresponding to Reaction Pathway</title>
<color>white</color>
<size>300</size>
<script>frame 1.23;vibration 1</script>
</jmolApplet></jmol>

The negative vibration frequency from the PM6 optimised structure for the transition state corresponds to the reaction path. Figure 3 shows that this negative frequency vibration is a symmetric stretch and therefore the formation of the two bonds is synchronous.

===Exercise 2:Reaction of Cyclohexadiene and 1,3-Dioxole===
====Reaction====
[[File:SP3815 Q2 MECH FINAL.jpg|center|x200px|200px|frame|Figure 4 Mechanism for the reaction between cyclohexadiene and 1,3-Dioxole]]

====Molecular Orbital Diagram====
[[File:SP3815_MO_FINAL_1.jpg|centre|600px|thumb|Figure 5 Molecular Orbital Diagram for the Formation of the Transition State]]
{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Symmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Endo Asymmetrical Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.30; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 40; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Symmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 42; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Exo Asymmetric Anti Bonding MO</title>
<color>white</color>
<size>200</size>
<script>frame 1.20; mo 43; mo nodots mesh fill translucent;mo cutoff 0.02; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" colspan="2" | Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
|
| PM6 Optimisation
| B3LYP/6-31G(d) Optimisation
|-
| 1,3-Dioxole
| -137.2505776
| -701188.4294
|-
| Cyclohexadiene
| 306.857803
| -612592.877
|-
| Endo Transition State
| 362.1665616
| -1313621.479
|-
| Endo Product
| 99.26223482
| -1313848.695
|-
| Exo Transition State
| 364.6870405
| -1313613.642
|-
| Exo Product
| 99.7085693
| -1313815.098
|-
| Endo Reaction Barrier
| 192.56
| 159.83
|-
| Endo Reaction Energy
| -70.34
| -67.39
|-
| Exo Reaction Barrier
| 195.08
| 167.66
|-
| Exo Reaction Energy
| -69.90
| -63.79
|}

The endo reaction barrier is 2.52 KJmol<sup>-1</sup> lower than the exo reaction barrier for the PM6 optimisation. Furthermore, the endo reaction barrier is 7.83 KJmol<sup>-1</sup> lower than the exo reaction barrier for the B3LYP/6-31G(d) optimisation. The Arrhenius equation (k=Aexp(-E<sub>a</sub>)/RT)) shows that as the activation energy for the formation of the endo product is lower than for the exo product, the rate at which the endo product is formed is greater than the rate at which the exo product is formed. Therefore the endo product is the kinetic product and is formed at room temperature under non-equilibrating conditions. The endo product forms at a faster rate due to the favourable bonding interactions between the developing π bond and the oxygen atoms of the 1,3-dioxole which decreases the energy of the transition state and hence lowers the activation energy. Figure 6 shows that there are favourable, bonding interactions between the p orbitals of the oxygen atoms of the 1,3-dioxole with the bonding π orbital of the new π bond in the HOMO of the endo transition state.

The endo product is 0.45 KJmol<sup>-1</sup> lower in energy than the exo product for the PM6 optimisation. Furthermore, the endo product is 33.60 KJmol<sup>-1</sup> lower in energy than the exo product for the B3LYP/6-31G(d) optimisation. The endo product is more stable than the exo product, therefore the endo product is also the thermodynamic product and will form under equilibrating conditions. Figure 7 shows that there is steric hindrance between the 1,3-dioxole ring and the two carbon bridge of the cyclohexadiene in the transition state. This steric hindrance increases energy of the transition state and therefore the activation and also increases the energy of the final exo product.

{| class="wikitable"
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_ENDO_TS_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 6 Secondary Interactions in the HOMO of Endo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.30; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
! <jmol><jmolApplet>
<uploadedFileContents>SP3815_EXO_TM_OPT_B3LYP.LOG</uploadedFileContents>
<script>frame 1.30</script>
<title>Figure 7 Secondary Interactions in the HOMO of Exo TS</title>
<color>white</color>
<size>300</size>
<script>frame 1.20; mo 41; mo nodots mesh fill translucent;mo cutoff 0.01; mo titleformat "";
</script>
</jmolApplet></jmol>
|}

===Exercise 3: Diels-Alder vs Cheletropic===
====Reaction====
[[File:SP3815_Q3_MECHANISM.jpg|center|500px|thumb|Figure 8 Two Possible Mechanisms for the reaction between Xylylene and SO<sub>2</sub>]]

====IRC====
[[File:SP3815 Q3 ENDO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Endo Product]]
[[File:SP3815 Q3 EXO IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Exo Product]]
[[File:SP3815 Q3 CHEL IRC.gif|center|600px|thumb|'''Figure 1''' IRC for the formation of the Cheletropic Product]]

====Thermochemistry====
{| class="wikitable"
! style="background: #0D4F8B; color: white;" |
! style="background: #0D4F8B; color: white;" |Sum of Electronic and Thermal Free Energies/KJmol<sup>-1</sup>
|-
| Xylylene
| 467.56455873
|-
| SO<sub>2</sub>
| -313.1406217
|-
| Diels Alder Endo TS
| 237.7651754
|-
| Diels Alder Endo Product
| 56.98645242
|-
| Diels Alder Exo TS
| 241.7428061
|-
| Diels Alder Exo Product
| 56.33007771
|-
| Cheletropic TS
| 260.0661626
|-
| Cheletropic Product
| 0.0131274942
|-
| Endo Reaction Barrier
| 83.34
|-
| Endo Reaction Energy
| -97.44
|-
| Exo Reaction Barrier
| 87.32
|-
| Exo Reaction Energy
| -98.19
|-
| Cheletropic Reaction Barrier
| 105.64
|-
| Cheletropic Reaction Energy
| -154.41
|}

====Reaction Profile====