==Introduction==

==Exercise 1: Reaction of Butadiene with Ethene==

[[File:R_E1_rwz15.PNG|350px|thumb|center|Figure 1: Reaction of Butadiene with Ethene]]

===Molecular Orbitals===

[[File:MO_E1_rwz15.PNG|450px|thumb|Figure 2: Molecular Orbital diagram showing the formation of the transition state of cyclohexene]]

Looking at the molecular orbitals of both the reactants and the transition state allows us to determine the interacting orbitals of the transition state. We can see from Table 1 below that both the HOMO and the LUMO of the transition state are formed from the HOMO of the ethene and the LUMO of the Butadiene, which are both symmetric. The HOMO of the Butadiene and the LUMO of the ethene, which are both antisymmetric also interact to give the HOMO-1 and the LUMO+1 of the transition state. As a result we can conclude that only orbitals of the same symmetry can interact to give new molecular orbitals, reactions are therefore only allowed when orbitals of the same symmetry can interact and so orbitals of opposite symmetry cannot interact and hence the reaction will be disallowed. The orbital overlap integral of symmetric-antisymmetric interaction is zero as they do not mix while both symmetric-symmetric and antisymmetric-antisymmetric interactions have a non-zero orbital overlap integral.

The molecular orbitals of the transition state are higher in energy than both the HOMOs of the reactants due to the reaction barrier that needs to be reached in order for a reaction to take place. The HOMO-1 of the Transition state has a greater contribution from the HOMO of Butadiene, while LUMO+1 has a greater contribution from the ethene showing that the LUMO of ethene is higher in energy than the HOMO of butadiene. The HOMO of the transition state has a larger contribution from the ethene HOMO and the LUMO of the transition state has a larger contribution from the LUMO of Butadiene. As the HOMO of the Butadiene and the LUMO of the Ethene are closest in energy, this is an example of an normal electron demand Diels-Alder reaction.
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|+ Table 1: MOs of Ethene, Butadiene and the transition state of cyclohexene
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===Carbon-Carbon bond lengths===

{| class="wikitable" border="1"
|+ Table 2: Lengths of Carbon Carbon bond at different stages of reaction (Å)
! Bonds
! Butadiene and Ethene
! Transition State
! Cyclohexene
|-
| '''C1-C2''' || 1.4708 || 1.4111 || 1.3370
|-
| '''C2-C3''' || 1.3334 || 1.3798 || 1.5008
|-
| '''C3-C4''' || - || 2.1148 || 1.5372
|-
| '''C4-C5''' || 1.3273 || 1.3818 || 1.5346
|-
| '''C5-C6''' || - || 2.1147 || 1.5371
|-
| '''C6-C1''' || 1.3334 || 1.3798 || 1.5008
|}

As the reaction proceeds, the single bond on Butadiene (C1-C2) shortens due to the carbons changing from sp<sub>3</sub> hybridised to sp<sub>2</sub> hybridised while the opposite is true for the ethene double bond (C4-C5) which lengthens as the hybridisation changes from sp<sub>2</sub> to sp<sub>3</sub>. Both the double bonds on Butadiene also lengthen as their sp<sub>2</sub> character is lost. The 2 bonds that form have a bond length that is within two times the van der waal radius of carbon of 1.7Å showing that the two molecules are starting to interacting during the transition state and once the bond forms they shorten to that of a single C-C bond.<ref>Bondi, A_. "van der Waals volumes and radii." The Journal of physical chemistry 68.3 (1964): 441-451. </ref> Typical C=C double bond lengths for ethene are normally around 1.3305Å and C-C single bonds lengths are 1.54Å.<ref>Craig, Norman C., Peter Groner, and Donald C. McKean. "Equilibrium structures for butadiene and ethylene: compelling evidence for π-electron delocalization in butadiene." The Journal of Physical Chemistry A 110.23 (2006): 7461-7469. </ref> These lengths match up to the cyclohexene product with bonds adjacent to the double bond being slightly shorter due to the pulling effects of the electron density.

===Transition State===

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The vibration shown above corresponds to the negative vibration of the transition state due to the negative force constant when calculating the frequency of vibrations. The formation of the 2 bonds is synchronous as the vibration shows that both ends of ethene and butadiene move together at the same time. Further proof is seen in the IRC where both bond are formed in the same frame.

[[Media:CYCLOHEXENE_PM6_TS_IRC_rwz15.LOG|log file of IRC]]

[[Media:rwz15_cyclohexene_pm6opt.LOG|log file of optimised cyclohexene product]]

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

[[File:R_E2_rwz15.PNG|350px|thumb|center|Figure 3: Reaction of Cyclohexadiene with 1,3-Dioxole]]

===Molecular Orbitals===

[[File:MO_E2f_rwz15.PNG|450px|thumb|Figure 4: Molecular Orbital diagram showing the formation of the transition state of Dioxole reacting with cyclohexadiene]]

Analysis of the Molecular Orbitals of the reactants and the transition states shows that this reaction is an inverse electron demand Diels-Alder reaction as the orbitals of the reactants which are closest in energy and hence interacts the most strongly are the HOMO of the Dioxole and the LUMO of the cyclohexadiene. This is possible because the oxygens on Dioxle can donate electron density into the double bond raising the energy of both the HOMO and LUMO of Dioxole compared to a normal ethene molecule. This causes the HOMO of the Dioxole to be closer in energy with the LUMO of the cyclohexadiene.

The large energy gap between the HOMO of cyclohexadiene and the LUMO of dioxole means that they only interact weakly, as a result in the transition state the HOMO -1 is only destabilised slightly and so the energy of the HOMO -1 does not move above the energies of the reactants. Like the reaction in exercise 1, this reaction can only occur if orbitals of the same symmetry interact, this is shown in table 3 below.
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===Thermochemistry===

[[File:2ndorbover.png|200px|thumb|right|Figure 5: Depiction of secondary overlap in the endo transition state]]

The thermochemistry data from the calculations enabled us to calculate the reaction barriers and energies which are shown in table 4 below. From the data we can see the endo transition state requires less energy to achieve than the exo, this is due to the secondary orbital overlap between the p orbitals of the oxygens and the pi system orbitals of the diene stabilising the transition state, showing that the endo product is the kinetic product. When considering the reaction energies, the endo product is also the thermodynamically more stable product and this can also be attributed to the secondary orbital overlap which still can be seen in the product. Another reason could be due to sterics, in the exo product the bridgehead could interact unfavourably with the carbon between the two oxygens which does not occur in the endo product. As a result, the data shows that the endo product is both the kinetically and thermodynamically more favourable product. The secondarry orbital overlap can be seen in figure 5 shown right.

{| class="wikitable" border="1"
|+ Table 4: Thermochemistry data
! Product
! Reaction Barrier KJmol<sup>-1</sup>
! Reaction Energy KJmol<sup>-1</sup>
|-
| Endo || 158.47 || -68.75
|-
| Exo || 166.30 || -65.15
|}

[[Media:rwz15_DIOXOLE_B3LYP.LOG|log file of optimised Dioxole]]

[[Media:rwz15_CYCLOHEXADIENE_B3LYP.LOG|log file of optimised cyclohexadiene]]

[[Media:rwz15_ENDO_prod_B3LYP.LOG|log file of optimised endo product]]

[[Media:rwz15_EXO_Prod_B3LYP.LOG|log file of optimised exo product]]

==Exercise 3: Reaction of o-Xylylene with SO<sub>2</sub>==

[[File:R_E3_rwz15.PNG|350px|thumb|Figure 6: Reaction of o-Xylylene with SO<sub>2</sub>]]

===IRCs===

{| class="wikitable" border="1"
|+ MOs of the reactants and the transition states
|-
|[[File:Rwz15Exo.gif|300px|thumb|Figure 1:exo]]||[[File:rwz15Endo.gif|300px|thumb|Figure 1:endo]]
||[[File:Cherwz15.gif|300px|thumb|Figure 1:cheal]]
|}

===Thermochemistry===

After calculating the reaction energies and barriers of the 3 possible products formed, it can be concluded that the kinetic product is the endo product due to it having the lowest reaction barrier so is more accessible, this is due to interaction between the non bonding oxygen and the diene of xylylene. The thermodynamic product is the cheletropic product as shown by its lowest reaction energy, this is due to the presence of the extra S=O bond which has a stronger bond energy than the combined energy of both C-O and S-O. The cheletropic product has the highest transition state due to the formation of a 5 membered ring compared to a 6 membered ring which is unfavourable due to ring strain.

Xylylene is highly reactive and unstable due to it wanting to form an aromatic ring structure to stabilise itself. This can be seen in the IRC where the aromatic ring forms before the bonds to SO2 forms.

{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Product
! Reaction Barrier
! Reaction Energy
|-
| ENDO || 81.73 || -99.05
|-
| EXO || 85.72 || -99.70
|-
| Cheal || 104.45 || -156.03
|}

[[File:Rwz15_rc.PNG|400px|thumb|Figure 1:few]]Rwz15_rc.PNG

===Alternative Diels-Alder Pathway===

{| class="wikitable" border="1"
|+ MOs of the reactants and the transition states
|-
|[[File:rwz15Exoalt.gif|300px|thumb|Figure 1:few]]||[[File:rwz15Endoalt.gif|300px|thumb|Figure 1:few]]
|}

o-xylylene can undergo diels-Alder reaction at an alternative site which is shown above. The thermochemistry data for these reactions show that energy would be require in order for reaction to occur, this is shown by a positive reaction energy. The reaction barriers are also much higher compared to the corresponding products at the other site. This is due to the reaction at this site which prevents aromatisation of the ring .

{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Product
! Reaction Barrier
! Reaction Energy
|-
| ENDO || 111.95 || 16.22
|-
| EXO || 119.79 || 20.68
|-
| other || - || -
|}

==Conclusion==

==References==

2017-11-22T02:02:53Z

2017-11-21T22:20:49Z

Rwz15:

==Introduction==

==Exercise 1: Reaction of Butadiene with Ethene==

===Molecular Orbitals===

[[File:R_E1_rwz15.PNG|350px|thumb|center|Figure 1:Reaction of Butadiene with Ethene]]
[[File:MO_E1_rwz15.PNG|450px|thumb|Figure 2:Molecular Orbital diagram showing the formation of the transition state of cyclohexene]]

Looking at the molecular orbitals of both the reactants and the transition state allows us to determine the orbitals of the reactants that interact to give the transition state. We can see from table 1 below that both the HOMO and the LUMO of the transition state are formed from the HOMO of the ethene and the LUMO of the Butadiene which are both symmetric. This is an example of a normal electron demand Diels-Alder reaction. The HOMO of the Butadiene and the LUMO of the ethene, which are both antisymmetric also interact to give the HOMO-1 and the LUMO+1 of the transition state. As a result we can conclude that only orbitals of the same symmetry can interact to give new molecular orbitals. The orbital overlap integral of symmetric-antisymmetric interaction is zero as they do not interact while both symmetric-symmetric and antisymmetric-antisymmetric have a non-zero orbital overlap integral.

The molecular orbitals of the transition state are higher in energy than both the HOMOs of the reactants due to the reaction barrier that needs to be reached in order for a reaction to take place. The HOMO-1 of the Transition state has a greater contribution from the HOMO of Butadiene, while LUMO+1 has a greater contribution from the ethene showing that the respective orbitals are closer and hence that the HOMO of butadiene is lower in energy than the LUMO of ethene which is a trait of normal electron demand Diels-Alder reactions.The HOMO of the transition state has a larger contribution from the ethene and the LUMO has a larger contribution from Butadiene.

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===Carbon carbon bond lengths===

{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Bonds
! Butadiene and Ethene
! Transition State
! Cyclohexene
|-
| '''C1-C2''' || 1.47078 || 1.41112 || 1.33696
|-
| '''C2-C3''' || 1.33343 || 1.37977 || 1.50084
|-
| '''C3-C4''' || -|| 2.11483 || 1.53715
|-
| '''C4-C5''' || 1.32731 || 1.38178 || 1.53462
|-
| '''C5-C6''' || - || 2.11470 || 1.53712
|-
| '''C6-C1''' || 1.33343 || 1.37980 || 1.50084
|}

As the reaction proceeds, the single bond on Butadiene (C1-C2) shortens as the reaction proceeds due to changing from sp<sub>3</sub> to sp<sub>2</sub> while the ethene double bond (C4-C5) lengthens as the hybridisation changes from sp<sub>2</sub> to sp<sub>3</sub>. Both the double bonds on Butadiene also lengthen as their sp<sub>2</sub> character is lost. The 2 bonds that form have a bond length that is within two times the van der waal radius of 1.7A showing that the two molecules are interacting during the transition state and once the bond forms they shorten to that of a single bond. Typical C-C double bonds are normally around 147A and C-C single bonds 154A.

===Transition State===

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The vibration shown above corresponds to the negative vibration of the transition state due to the negative force constant when calculating the frequency of vibrations. The formation of the 2 bonds is synchronous as in the vibration shown above both the ends of ethene and butadiene move together at the same time. Further proof is seen in the IRC where both bond are formed in the same frame.
[[Media:CYCLOHEXENE_PM6_TS_IRC_rwz15.LOG|log file of IRC]]
[[Media:rwz15_cyclohexene_pm6opt.LOG|log file of cyclohexene product]]
==Exercise 2==

[[File:R_E2_rwz15.PNG|350px|thumb|Figure 1:Reaction of Butadiene with Ethene]]
[[File:MO_E2_rwz15.PNG|450px|thumb|Figure 2:Molecular Orbital diagram showing the formation of the transition state of cyclohexene]]

Due to the electron donating ability of oxygens on the dioxole, the dieneophile is electron rich and thus raises the energy of both its HOMO and LUMO. This causes the LUMO of the cyclohexadiene (diene) to be able to interact with the HOMO of dioxole. This is known as an inverse electron demand Diels-Alder reaction. The large energy gap between the HOMO of cyclohexadiene and the LUMO of the dioxole means that they only interact weakly, as a result in the transition state the HOMO -1 and the LUMO +1 are only destabilised slightly and so the energy of the HOMO -1 does not move above the energies of the reactants.

The transition state molecular orbitals of both the endo and exo products are symmetrical as shown in table 2 below.

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|EXO HOMO-1||EXO HOMO||EXO LUMO||EXO LUMO+1
|}

The thermochemistry data from the calculations enabled us to calculate the reaction barriers and energies which are shown in table 3 below. From this data we can see the endo transition state requires less energy to reach than the exo, this is due to the secondary orbital overlap between the p orbitals of the oxygens and the pi* orbitals of the diene stabilising the transition state. When considering the reaction energies, the endo product is also the thermodynamically more stable product and it can also be attributed to the secondary orbital overlap which still can be seen in the product.Another reason could be due to sterics, in the exo product the bridgehead could interact unfavourably with the carbon between the two oxygens which does not occur in the endo product. As a result the data shows that the endo product is both the kinetically and thermodynamically more favourable product. The secondarry orbital overlap can be seen in figure 5 shown below

[[File:2ndorbover.png|300px|thumb|Figure 1:few]]
{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Product
! Reaction Barrier
! Reaction Energy
|-
| ENDO || 158.47 || -68.75
|-
| EXO || 166.30 || -65.15
|}

==Exercise 3==

{| class="wikitable" border="1"
|+ MOs of the reactants and the transition states
|-
|[[File:Rwz15Exo.gif|300px|thumb|Figure 1:exo]]||[[File:rwz15Endo.gif|300px|thumb|Figure 1:endo]]
||[[File:Cherwz15.gif|300px|thumb|Figure 1:cheal]]
|}

After calculating the reaction energies and barriers of the 3 possible products formed, it can be concluded that the kinetic product is the endo product due to it having the lowest reaction barrier so is more accessible, this is due to interaction between the non bonding oxygen and the diene of xylylene. The thermodynamic product is the cheletropic product as shown by its lowest reaction energy, this is due to the presence of the extra S=O bond which has a stronger bond energy than the combined energy of both C-O and S-O. The cheletropic product has the highest transition state due to the formation of a 5 membered ring compared to a 6 membered ring which is unfavourable due to ring strain.

Xylylene is highly reactive and unstable due to it wanting to form an aromatic ring structure to stabilise itself. This can be seen in the IRC where the aromatic ring forms before the bonds to SO2 forms.

{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Product
! Reaction Barrier
! Reaction Energy
|-
| ENDO || 81.73 || -99.05
|-
| EXO || 85.72 || -99.7
|-
| Cheal || 104.45 || -156.03
|}

[[File:Rwz15_rc.PNG|400px|thumb|Figure 1:few]]Rwz15_rc.PNG

{| class="wikitable" border="1"
|+ MOs of the reactants and the transition states
|-
|[[File:rwz15Exoalt.gif|300px|thumb|Figure 1:few]]||[[File:rwz15Endoalt.gif|300px|thumb|Figure 1:few]]
|}

o-xylylene can undergo diels-Alder reaction at an alternative site which is shown above. The thermochemistry data for these reactions show that energy would be require in order for reaction to occur, this is shown by a positive reaction energy. The reaction barriers are also much higher compared to the corresponding products at the other site. This is due to the reaction at this site which prevents aromatisation of the ring .

{| class="wikitable" border="1"
|+ Reaction trajectories with varying momenta
! Product
! Reaction Barrier
! Reaction Energy
|-
| ENDO || 111.95 || 16.22
|-
| EXO || 119.79 || 20.68
|-
| other || - || -
|}

==Conclusion==