== Introduction<ref><nowiki>https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise</nowiki></ref> ==
Gaussian can been used to locate and characterize transition structures for a variety of pericyclic reactions. It is able to optimize the molecular geometry and calculate the vibrational frequency of a compound based on Born Oppenheimer approximation where the electronic distribution of a molecule move instantaneously to the movement of nuclei. Potential energy surface can be plotted using quantum chemistry by calculating the energy as a function of positions of the nuclei.

Geometry optimization will lead to a local minimum which may be a global minimum or a transition state of the product. We can tell which of the minimum we got using to methods.
First, we can tell from the potential energy surface(PES). For a global minimum, energy will rise in all direction from that point of minimum on the PES. Whereas for a transition state, the energy will decrease in one direction which is the reaction path on the PES.
Secondly, by performing a frequency calculation on Gaussian. For a global minimum, we will have all positive frequency whereas for a transition state we will have one imaginary frequency which is due to the negative value of secondary derivative of energy(a maximum on the PES). <ref><nowiki>Lecture notes: Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Michael Bearpark, Imperial College.</nowiki></ref>

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732Å
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526Å
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834Å
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977Å, C2C3=1.41110Å
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177Å
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478Å
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702Å, C1C2=1.50077Å, C3C4=1.50095Å
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711Å, C2C3=1.53450Å, C3C4=1.53720Å
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 Å and 1.337 Å <ref><nowiki>Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</nowiki></ref>.
The Van der Waals radii of carbon is 1.7 Å <ref><nowiki>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</nowiki></ref>.
The interatomic distance between the reacting carbons (2.11 Å) are shorter than the Van der Waals radii (3.4 Å). This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene(IRC)!! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 101.44 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 81.56 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 103.86 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

Xylylene is unstable and this can be proven by its high Gibbs free energy. According to the IRC pathway, after the bonding of the 6-membered ring the energy of the product drops. This is due to the formation of delocalised pi system that forms resonance which lowers the energy of the product.

=== Reaction Profile ===
[[File:Reaction profile wtc.png|600px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

=== Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies second cis-butadiene fragment in o-xylylene
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.065610 || 0.102066 || 111.77 || 16.05
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 ||0.067304 || 0.105053 || 119.61 || 20.50
|-
| colspan=8 |(Table 9:Values of the sum of electronic and thermal Free Energies for second cis-butadiene fragment in o-xylylene, calculation ran at semi-empirical(PM6))
|}

The endo(0.067304 kJ/mol) and exo(0.065610 kJ/mol) products of Diels-Alder Reaction between second cis-butadiene fragment in o-xylylene and SO<sub>2</sub> are unfavourable because both has higher energy than the reactants (0.059495 kJ/mol).

== Conclusion ==

The partly formed C-C bonds in the TS of the reaction between butadiene and ethene is shorter than the Van der Waals radii(3.4 Å). This shows that the reacting carbon from butadiene and ethene are approaching together to form a bond. Along the reaction, all double bond shortens to form single bond and all single bond elongate to form double bond. New bonds are formed between the reacting carbons at the same time for the Diels-Alder reaction between butadiene and ethene, therefore it is a synchronous reaction.

The endo product of the reaction between cyclopentadiene and 1,3-dioxole is kinetically and thermodynamically favoured product because the secondary interaction between the p orbital of oxygen in 1,3-dioxole and p orbital of diene provides extra stability of product in the formation of transition state. The exo product has higher energy than expected due to steric problem caused by the sp3 carbon centres of both cyclohexene and 1,3-dioxole. From the HOMO of TS from table 5, it is clearly dominated by the HOMO of 1,3-dioxole(dienophile). The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric.

Diels Alder reaction between xylylene and SO<sub>2</sub> will only occur at the outer cis butadiene fragment of the xylylene. The product obtained through the reaction with the second cis-butadiene fragment in o-xylylene is unfavourable because the it has higher energy than the reactant which might due to increase steric hindrance of the product compare to it's reactants.

== Reference ==

File:Reaction profile wtc.png

2016-11-29T14:09:31Z

Wtc14:

Rep:Wtc14

2016-11-29T13:55:21Z

Wtc14: /* Reaction Path */

== Introduction<ref><nowiki>https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise</nowiki></ref> ==
Gaussian can been used to locate and characterize transition structures for a variety of pericyclic reactions. It is able to optimize the molecular geometry and calculate the vibrational frequency of a compound based on Born Oppenheimer approximation where the electronic distribution of a molecule move instantaneously to the movement of nuclei. Potential energy surface can be plotted using quantum chemistry by calculating the energy as a function of positions of the nuclei.

Geometry optimization will lead to a local minimum which may be a global minimum or a transition state of the product. We can tell which of the minimum we got using to methods.
First, we can tell from the potential energy surface(PES). For a global minimum, energy will rise in all direction from that point of minimum on the PES. Whereas for a transition state, the energy will decrease in one direction which is the reaction path on the PES.
Secondly, by performing a frequency calculation on Gaussian. For a global minimum, we will have all positive frequency whereas for a transition state we will have one imaginary frequency which is due to the negative value of secondary derivative of energy(a maximum on the PES). <ref><nowiki>Lecture notes: Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Michael Bearpark, Imperial College.</nowiki></ref>

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732Å
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526Å
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834Å
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977Å, C2C3=1.41110Å
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177Å
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478Å
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702Å, C1C2=1.50077Å, C3C4=1.50095Å
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711Å, C2C3=1.53450Å, C3C4=1.53720Å
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 Å and 1.337 Å <ref><nowiki>Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</nowiki></ref>.
The Van der Waals radii of carbon is 1.7 Å <ref><nowiki>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</nowiki></ref>.
The interatomic distance between the reacting carbons (2.11 Å) are shorter than the Van der Waals radii (3.4 Å). This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene(IRC)!! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 101.44 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 81.56 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 103.86 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

Xylylene is unstable and this can be proven by its high Gibbs free energy. According to the IRC pathway, after the bonding of the 6-membered ring the energy of the product drops. This is due to the formation of delocalised pi system that forms resonance which lowers the energy of the product.

=== Reaction Profile ===
[[File:Energy profile wtc.png|500px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

=== Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies second cis-butadiene fragment in o-xylylene
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.065610 || 0.102066 || 111.77 || 16.05
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 ||0.067304 || 0.105053 || 119.61 || 20.50
|-
| colspan=8 |(Table 9:Values of the sum of electronic and thermal Free Energies for second cis-butadiene fragment in o-xylylene, calculation ran at semi-empirical(PM6))
|}

The endo(0.067304 kJ/mol) and exo(0.065610 kJ/mol) products of Diels-Alder Reaction between second cis-butadiene fragment in o-xylylene and SO<sub>2</sub> are unfavourable because both has higher energy than the reactants (0.059495 kJ/mol).

== Conclusion ==

The partly formed C-C bonds in the TS of the reaction between butadiene and ethene is shorter than the Van der Waals radii(3.4 Å). This shows that the reacting carbon from butadiene and ethene are approaching together to form a bond. Along the reaction, all double bond shortens to form single bond and all single bond elongate to form double bond. New bonds are formed between the reacting carbons at the same time for the Diels-Alder reaction between butadiene and ethene, therefore it is a synchronous reaction.

The endo product of the reaction between cyclopentadiene and 1,3-dioxole is kinetically and thermodynamically favoured product because the secondary interaction between the p orbital of oxygen in 1,3-dioxole and p orbital of diene provides extra stability of product in the formation of transition state. The exo product has higher energy than expected due to steric problem caused by the sp3 carbon centres of both cyclohexene and 1,3-dioxole. From the HOMO of TS from table 5, it is clearly dominated by the HOMO of 1,3-dioxole(dienophile). The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric.

Diels Alder reaction between xylylene and SO<sub>2</sub> will only occur at the outer cis butadiene fragment of the xylylene. The product obtained through the reaction with the second cis-butadiene fragment in o-xylylene is unfavourable because the it has higher energy than the reactant which might due to increase steric hindrance of the product compare to it's reactants.

== Reference ==

Rep:Wtc14

2016-11-29T13:53:04Z

Wtc14: /* Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene */

== Introduction<ref><nowiki>https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise</nowiki></ref> ==
Gaussian can been used to locate and characterize transition structures for a variety of pericyclic reactions. It is able to optimize the molecular geometry and calculate the vibrational frequency of a compound based on Born Oppenheimer approximation where the electronic distribution of a molecule move instantaneously to the movement of nuclei. Potential energy surface can be plotted using quantum chemistry by calculating the energy as a function of positions of the nuclei.

Geometry optimization will lead to a local minimum which may be a global minimum or a transition state of the product. We can tell which of the minimum we got using to methods.
First, we can tell from the potential energy surface(PES). For a global minimum, energy will rise in all direction from that point of minimum on the PES. Whereas for a transition state, the energy will decrease in one direction which is the reaction path on the PES.
Secondly, by performing a frequency calculation on Gaussian. For a global minimum, we will have all positive frequency whereas for a transition state we will have one imaginary frequency which is due to the negative value of secondary derivative of energy(a maximum on the PES). <ref><nowiki>Lecture notes: Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Michael Bearpark, Imperial College.</nowiki></ref>

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732Å
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526Å
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834Å
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977Å, C2C3=1.41110Å
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177Å
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478Å
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702Å, C1C2=1.50077Å, C3C4=1.50095Å
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711Å, C2C3=1.53450Å, C3C4=1.53720Å
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 Å and 1.337 Å <ref><nowiki>Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</nowiki></ref>.
The Van der Waals radii of carbon is 1.7 Å <ref><nowiki>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</nowiki></ref>.
The interatomic distance between the reacting carbons (2.11 Å) are shorter than the Van der Waals radii (3.4 Å). This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 101.44 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 81.56 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 103.86 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

Xylylene is unstable and this can be proven by its high Gibbs free energy. According to the IRC pathway, after the bonding of the 6-membered ring the energy of the product drops. This is due to the formation of delocalised pi system that forms resonance which lowers the energy of the product.

=== Reaction Profile ===
[[File:Energy profile wtc.png|500px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

=== Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies second cis-butadiene fragment in o-xylylene
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.065610 || 0.102066 || 111.77 || 16.05
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 ||0.067304 || 0.105053 || 119.61 || 20.50
|-
| colspan=8 |(Table 9:Values of the sum of electronic and thermal Free Energies for second cis-butadiene fragment in o-xylylene, calculation ran at semi-empirical(PM6))
|}

The endo(0.067304 kJ/mol) and exo(0.065610 kJ/mol) products of Diels-Alder Reaction between second cis-butadiene fragment in o-xylylene and SO<sub>2</sub> are unfavourable because both has higher energy than the reactants (0.059495 kJ/mol).

== Conclusion ==

The partly formed C-C bonds in the TS of the reaction between butadiene and ethene is shorter than the Van der Waals radii(3.4 Å). This shows that the reacting carbon from butadiene and ethene are approaching together to form a bond. Along the reaction, all double bond shortens to form single bond and all single bond elongate to form double bond. New bonds are formed between the reacting carbons at the same time for the Diels-Alder reaction between butadiene and ethene, therefore it is a synchronous reaction.

The endo product of the reaction between cyclopentadiene and 1,3-dioxole is kinetically and thermodynamically favoured product because the secondary interaction between the p orbital of oxygen in 1,3-dioxole and p orbital of diene provides extra stability of product in the formation of transition state. The exo product has higher energy than expected due to steric problem caused by the sp3 carbon centres of both cyclohexene and 1,3-dioxole. From the HOMO of TS from table 5, it is clearly dominated by the HOMO of 1,3-dioxole(dienophile). The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric.

Diels Alder reaction between xylylene and SO<sub>2</sub> will only occur at the outer cis butadiene fragment of the xylylene. The product obtained through the reaction with the second cis-butadiene fragment in o-xylylene is unfavourable because the it has higher energy than the reactant which might due to increase steric hindrance of the product compare to it's reactants.

== Reference ==

Rep:Wtc14

2016-11-29T13:50:49Z

Wtc14: /* Introduction */

== Introduction<ref><nowiki>https://wiki.ch.ic.ac.uk/wiki/index.php?title=Mod:ts_exercise</nowiki></ref> ==
Gaussian can been used to locate and characterize transition structures for a variety of pericyclic reactions. It is able to optimize the molecular geometry and calculate the vibrational frequency of a compound based on Born Oppenheimer approximation where the electronic distribution of a molecule move instantaneously to the movement of nuclei. Potential energy surface can be plotted using quantum chemistry by calculating the energy as a function of positions of the nuclei.

Geometry optimization will lead to a local minimum which may be a global minimum or a transition state of the product. We can tell which of the minimum we got using to methods.
First, we can tell from the potential energy surface(PES). For a global minimum, energy will rise in all direction from that point of minimum on the PES. Whereas for a transition state, the energy will decrease in one direction which is the reaction path on the PES.
Secondly, by performing a frequency calculation on Gaussian. For a global minimum, we will have all positive frequency whereas for a transition state we will have one imaginary frequency which is due to the negative value of secondary derivative of energy(a maximum on the PES). <ref><nowiki>Lecture notes: Quantum Mechanics 3/3rd Year Computational Chemistry Laboratory, Michael Bearpark, Imperial College.</nowiki></ref>

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732Å
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526Å
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834Å
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977Å, C2C3=1.41110Å
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177Å
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478Å
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702Å, C1C2=1.50077Å, C3C4=1.50095Å
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711Å, C2C3=1.53450Å, C3C4=1.53720Å
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 Å and 1.337 Å <ref><nowiki>Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</nowiki></ref>.
The Van der Waals radii of carbon is 1.7 Å <ref><nowiki>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</nowiki></ref>.
The interatomic distance between the reacting carbons (2.11 Å) are shorter than the Van der Waals radii (3.4 Å). This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 101.44 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 81.56 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 103.86 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

Xylylene is unstable and this can be proven by its high Gibbs free energy. According to the IRC pathway, after the bonding of the 6-membered ring the energy of the product drops. This is due to the formation of delocalised pi system that forms resonance which lowers the energy of the product.

=== Reaction Profile ===
[[File:Energy profile wtc.png|500px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

=== Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies second cis-butadiene fragment in o-xylylene
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.065610 || 0.102066 || 111.77 || 16.05
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 ||0.067304 || 0.105053 || 119.61 || 20.50
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies for second cis-butadiene fragment in o-xylylene, calculation ran at semi-empirical(PM6))
|}

The endo(0.067304 kJ/mol) and exo(0.065610 kJ/mol) products of Diels-Alder Reaction between second cis-butadiene fragment in o-xylylene and SO<sub>2</sub> are unfavourable because both has higher energy than the reactants (0.059495 kJ/mol).
== Conclusion ==

The partly formed C-C bonds in the TS of the reaction between butadiene and ethene is shorter than the Van der Waals radii(3.4 Å). This shows that the reacting carbon from butadiene and ethene are approaching together to form a bond. Along the reaction, all double bond shortens to form single bond and all single bond elongate to form double bond. New bonds are formed between the reacting carbons at the same time for the Diels-Alder reaction between butadiene and ethene, therefore it is a synchronous reaction.

The endo product of the reaction between cyclopentadiene and 1,3-dioxole is kinetically and thermodynamically favoured product because the secondary interaction between the p orbital of oxygen in 1,3-dioxole and p orbital of diene provides extra stability of product in the formation of transition state. The exo product has higher energy than expected due to steric problem caused by the sp3 carbon centres of both cyclohexene and 1,3-dioxole. From the HOMO of TS from table 5, it is clearly dominated by the HOMO of 1,3-dioxole(dienophile). The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric.

Diels Alder reaction between xylylene and SO<sub>2</sub> will only occur at the outer cis butadiene fragment of the xylylene. The product obtained through the reaction with the second cis-butadiene fragment in o-xylylene is unfavourable because the it has higher energy than the reactant which might due to increase steric hindrance of the product compare to it's reactants.

== Reference ==

Rep:Wtc14

2016-11-29T13:46:39Z

Wtc14: /* Reference */

== Introduction ==
Gaussian can been used to locate and characterize transition structures for a variety of pericyclic reactions. It is able to optimize the molecular geometry and calculate the vibrational frequency of a compound based on Born Oppenheimer approximation where the electronic distribution of a molecule move instantaneously to the movement of nuclei. Potential energy surface can be plotted using quantum chemistry by calculating the energy as a function of positions of the nuclei.

Geometry optimization will lead to a local minimum which may be a global minimum or a transition state of the product. We can tell which of the minimum we got using to methods.
First, we can tell from the potential energy surface(PES). For a global minimum, energy will rise in all direction from that point of minimum on the PES. Whereas for a transition state, the energy will decrease in one direction which is the reaction path on the PES.
Secondly, by performing a frequency calculation on Gaussian. For a global minimum, we will have all positive frequency whereas for a transition state we will have one imaginary frequency which is due to the negative value of secondary derivative of energy(a maximum on the PES).

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732Å
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526Å
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834Å
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977Å, C2C3=1.41110Å
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177Å
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478Å
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702Å, C1C2=1.50077Å, C3C4=1.50095Å
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711Å, C2C3=1.53450Å, C3C4=1.53720Å
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 Å and 1.337 Å <ref><nowiki>Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</nowiki></ref>.
The Van der Waals radii of carbon is 1.7 Å <ref><nowiki>Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</nowiki></ref>.
The interatomic distance between the reacting carbons (2.11 Å) are shorter than the Van der Waals radii (3.4 Å). This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 101.44 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 81.56 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 103.86 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

Xylylene is unstable and this can be proven by its high Gibbs free energy. According to the IRC pathway, after the bonding of the 6-membered ring the energy of the product drops. This is due to the formation of delocalised pi system that forms resonance which lowers the energy of the product.

=== Reaction Profile ===
[[File:Energy profile wtc.png|500px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

=== Diels-Alder Reaction for the second cis-butadiene fragment in o-xylylene ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies second cis-butadiene fragment in o-xylylene
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.065610 || 0.102066 || 111.77 || 16.05
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 ||0.067304 || 0.105053 || 119.61 || 20.50
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies for second cis-butadiene fragment in o-xylylene, calculation ran at semi-empirical(PM6))
|}

The endo(0.067304 kJ/mol) and exo(0.065610 kJ/mol) products of Diels-Alder Reaction between second cis-butadiene fragment in o-xylylene and SO<sub>2</sub> are unfavourable because both has higher energy than the reactants (0.059495 kJ/mol).
== Conclusion ==

The partly formed C-C bonds in the TS of the reaction between butadiene and ethene is shorter than the Van der Waals radii(3.4 Å). This shows that the reacting carbon from butadiene and ethene are approaching together to form a bond. Along the reaction, all double bond shortens to form single bond and all single bond elongate to form double bond. New bonds are formed between the reacting carbons at the same time for the Diels-Alder reaction between butadiene and ethene, therefore it is a synchronous reaction.

The endo product of the reaction between cyclopentadiene and 1,3-dioxole is kinetically and thermodynamically favoured product because the secondary interaction between the p orbital of oxygen in 1,3-dioxole and p orbital of diene provides extra stability of product in the formation of transition state. The exo product has higher energy than expected due to steric problem caused by the sp3 carbon centres of both cyclohexene and 1,3-dioxole. From the HOMO of TS from table 5, it is clearly dominated by the HOMO of 1,3-dioxole(dienophile). The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric.

Diels Alder reaction between xylylene and SO<sub>2</sub> will only occur at the outer cis butadiene fragment of the xylylene. The product obtained through the reaction with the second cis-butadiene fragment in o-xylylene is unfavourable because the it has higher energy than the reactant which might due to increase steric hindrance of the product compare to it's reactants.

== Reference ==

2016-11-28T15:38:24Z

Wtc14: Wtc14 uploaded a new version of File:Energy profile wtc.png

Rep:Wtc14

2016-11-28T15:31:35Z

Wtc14: /* Energy Profile */

== Introduction ==

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732A
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526A
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834A
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977A, C2C3=1.41110A
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177A
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478A
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702A, C1C2=1.50077A, C3C4=1.50095A
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711A, C2C3=1.53450A, C3C4=1.53720A
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 A and 1.337 A <ref name="Bond Length" />
The Van der Waals raddi of carbon is 1.7A <ref name="VDW" />
The interatomic distance between the reacting carbons are shorter than the Van der Waals radii. This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
=== Intrinsic Reaction Coordinate ===
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|500px]]
| [[File:Product exo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|400px]]
|-
| colspan=5 | Backward Diels-Alder Path of Exo product.
|-
| || Endo || [[File:Endo product TS wtc.png|500px]]
| [[File:Product endo ric.gif|500px]]
| [[File:Diels alder irc reaction pathway endo.png|400px]]
|-
| colspan=5 | Foward Diels-Alder Path of endo product.
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|500px]]
| [[File:Cheletropic ric wtc.gif|500px]]
| [[File:Cheletropic ric rxn pathway.png|400px]]
|-
| colspan=5 | Forward cheletropic reaction
|-
|colspan=5 | Table 7: Transition state and IRC of Diels-Alder and cheletropic pathway.
|}

=== Energy Profile ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Xylylene(Hatree)
| '''SO<sub>2</sub> (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021455 || 0.092074 || 187.16 || -99.87
|-
| '''endo Diels-Alder''' || 0.178764 || -0.119269 || 0.059495 || 0.021695 || 0.090560 || 180.81 || -99.24
|-
| '''Cheletropic''' || 0.178764 || -0.119269 || 0.059495 || 0.000005 || 0.099055 || 260.06 || -156.19
|-
| colspan=8 |(Table 8:Values of the sum of electronic and thermal Free Energies, calculation ran at semi-empirical(PM6))
|}

The energy of reactant is calculated by adding both the energy of SO<sub>2</sub> and xylylene. (In vacuum, no interaction between xylylene and SO<sub>2</sub>.)
Compare to the exo product in exercise 2, there is no steric problem in the exo product. For the diels-Alder pathway, the exo product has a lower energy than the endo product, hence it is the thermodynamically favoured product.
The energy barrier(activation energy) of the exo product is higher that the endo product. Therefore, endo product is the kinetically favoured product.
Due to small difference between the endo and exo product, and with the secondary interaction between the p orbital of the oxygen in the SO<sub>2</sub> and the p orbital of the diene, the endo product will probably be the major product.
Within Diels-Alder product and cheletropic product, the energy barrier of cheletropic product is around 79 kJ/mol higher than the Diels-Alder product but the cheletropic product has a much lower energy than the Diels-Alder product. Hence, the Diels-Alder pathway is more preferred at low temperature and the cheletropic pathway is more preferred at high temperature so that it has enough energy to overcome the high activation energy.

=== Energy Profile ===
[[File:Energy profile wtc.png|500px]]

Diagram 2: Energy profile between Dielse-Alder pathway and cheletropic pathway.

== Conclusion ==

== Reference ==
<ref name="bondlength">Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</ref>

<ref name="VDW">Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</ref>

2016-11-28T13:22:44Z

Wtc14: /* Exercise 3 */

== Introduction ==

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732A
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526A
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834A
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977A, C2C3=1.41110A
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177A
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478A
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702A, C1C2=1.50077A, C3C4=1.50095A
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711A, C2C3=1.53450A, C3C4=1.53720A
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 A and 1.337 A <ref name="Bond Length" />
The Van der Waals raddi of carbon is 1.7A <ref name="VDW" />
The interatomic distance between the reacting carbons are shorter than the Van der Waals radii. This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|-
|colspan=3 |Table 3: Vibration of Trasition State.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|-
|colspan=2 | Table 4: Reaction path of cyclohexene
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=3 |Table 5: Transition state MO from cyclohexene and 1,3-dioxole.
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Table 6:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))

|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==
{| class="wikitable" border="1"
|+ Transition State of o-Xylylene-SO2 Cycloaddition
! Reaction !! Type of Product !! Transition state !! IRC !! Total Energy along IRC
|-
| Diels-Alder || Exo || [[File:Exo product TS wtc.png|600px]]
| [[File:Product exo ric.gif|600px]]
| [[File:Diels alder irc reaction pathway exo wtc.png|600px]]
|-
| || Endo || [[File:Endo product TS wtc.png|600px]]
| [[File:Product endo ric.gif|600px]]
| [[File:Diels alder irc reaction pathway endo.png|600px]]
|-
| Cheletropic || - || [[File:Cheletropic TS wtc.png|600px]]
| [[File:Cheletropic ric wtc.gif|600px]]
| [[File:Cheletropic ric rxn pathway.png|600px]]
|}

== Conclusion ==

== Reference ==
<ref name="bondlength">Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</ref>

<ref name="VDW">Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</ref>

File:Cheletropic ric rxn pathway.png

2016-11-28T13:22:20Z

Wtc14:

File:Diels alder irc reaction pathway exo wtc.png

2016-11-28T13:20:28Z

Wtc14:

2016-11-25T16:03:13Z

Wtc14: /* Bond Length Measurement */

== Introduction ==

== Exercise 1 ==
=== MO diagram for the formation of butadiene/ethene TS ===
[[File:MO wtc.png|700px]]
Diagram 1: MO diagram for the formation of the butadiene/ethene TS.
{| class="wikitable" border="1"
|+ MOs:
! Name of Compound !! Orbital !! Symmetry !! MO Images !! JMol Images
|-
| Ethene || HOMO || u || [[File:Ethene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Ethene || LUMO || g || [[File:Ethene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 12; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETHENE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || HOMO || g || [[File:Butadiene HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Butadiene || LUMO || u || [[File:Butadiene LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 22; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>DIENOPHILE OPT.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || second HOMO || N/A || [[File:TS 2nd HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || HOMO || N/A || [[File:TS HOMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || LUMO || N/A || [[File:TS LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| TS || Second LUMO || N/A || [[File:TS 2nd LUMO wtc.png|150px]]
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
|colspan=5 |Table 1: MOs of the reactants and TS.
|}
Symmetry of the reacting orbitals of both reactants must be the same for the reaction to be allowed. The HOMO of butadiene(g) interact with the LUMO of ethene(g) to produce the second HOMO and second LUMO of TS. LUMO of butadiene(u) interact with the HOMO of ethene(u) to produce the HOMO and LUMO of the TS. The overlap integral equals to 1 for same symmetry overlap of orbitals(ie ungerand-ungerand orbitals and gerand-gerand orbitals) and equals to 0 for different symmetry overlap of orbitals(ie gerand-ungerand orbitals and vice versa).

=== Bond Length Measurement ===

{| class="wikitable" border="1"
|+ Bond Length
! Compound !! Images !! Bond Length
|-
| Ethene || [[File:Ethene bondlength wtc.png|300px]] || C1C2=1.32732A
|-
| Butadiene || [[File:Butadiene bondlength 1234.png|300px]] || C1C2=C3C4=1.33526A
|-
| Butadiene || [[File:Butadiene bondlength 1.png|300px]] || C1C2=1.46834A
|-
| TS || [[File:TS bondlength.png|300px]] || C1C2=C3C4=1.37977A, C2C3=1.41110A
|-
| TS || [[File:TS bondlength 1.png|300px]] || C1C2=1.38177A
|-
| TS || [[File:TS bondlength 2.png|300px]] || C1C2=C3C4=2.11478A
|-
| Product || [[File:Product bondlength 1.png|300px]] || C2C3=1.33702A, C1C2=1.50077A, C3C4=1.50095A
|-
| Product || [[File:Butadiene bondlength 2.png|300px]] || C1C2=1.53711A, C2C3=1.53450A, C3C4=1.53720A
|-
|colspan=8 | Table 2: Bond length measurements.
|}

All double bonds elongate to form a single bond and all single bonds shorten to form a double bond
Typical sp3 and sp2 C-C bond lengths are 1.544 A and 1.337 A <ref name="Bond Length" />
The Van der Waals raddi of carbon is 1.7A <ref name="VDW" />
The interatomic distance between the reacting carbons are shorter than the Van der Waals radii. This means that the reacting carbons are approaching each other to react.

=== Vibration ===

{| class="wikitable" border="1"
|+ Vibration
! Type of Frequency !! Vibration !! Description
|-
| Imaginary Frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 17; vibration 2;</script>
</jmolApplet>
</jmol>
| The imaginary frequency is taken from the negative frequency. It shows the vibration mode that lead to the transition state of the reaction. Stretching of C=C and shortening of C-C bonds in both reactants can be seen. This compliments to the trend of the change in bond lengths from reactants to the final product shown above. There is also an out-of-plane bend involving the reaction centres, bring the terminal carbons of butadiene and ethene close together to form bonds.
|-
| Lowest positive frequency
|<jmol>
<jmolApplet>
<uploadedFileContents>CYCLOHEXENE TS PM6.LOG</uploadedFileContents>
<color>black</color>
<script>frame 18; vibration 2;</script>
</jmolApplet>
</jmol>
| From the vibration,the reacting centers do not approach each other in the vibration and hence does not lead to the reaction taking place.
|}

=== Reaction Path ===
{| class="wikitable" border="1"
|+ Reaction Path
! Formation of Cyclohaxene !! Energy Curve
|-
| [[File:Reaction path movie.gif|350px]] || [[File:Reaction path of cyclohexene.png|350px]]
|}
The formation of cyclohexene is synchronous because the bond between the reacting centers break at the same time. This can be proved by the presence of a single maximum in the potential energy curve.

== Exercise 2 ==
=== Transition State MO ===
{| class="wikitable" border="1"
|+ Molecular Orbitals
! Type of Product !! MO !! Transition State MO
|-
| Exo Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| Exo Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>Cyclo dioxo exo b3lyp jmol.log</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; mo cutoff 0.02</script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second HOMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|-
| ENDO Product || Second LUMO
|<jmol>
<jmolApplet>
<color>white</color>
<size>200</size>
<script>frame 1.6; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; </script>
<uploadedFileContents>CYCLO DIOXOLE TS B3LYP JMOL.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

The HOMO and LUMO TS of both exo and endo products are symmetric because they are formed by HOMO of dienophile and LUMO of diene that are also symmetric. Whereas both the LUMO of dienophile(antisymmetric)and HOMO of the diene(antisymmetric) form the second HOMO and second LUMO of the TS which are both antisymmetric.
The HOMO of transition state is formed between the HOMO of 1,3-dioxole(dienophile) and the LUMO of hexacyclodiene(diene). From the HOMO TS shown above the orbitals of 1,3-dioxole dominate over the orbitals from hexacyclodiene. This is because 1,3-dioxole has electron donating groups that pulls up the potential energy of the HOMO of 1,3-dioxole. Therefore, this reaction is an inverse electron demand Diels-Alder reaction.

=== Thermochemistry ===
{| class="wikitable" border="1"
|+ Sum of electronic and thermal Free Energies
! !! Cyclopentadiene(Hatree)
| '''1,3-dioxole (Hatree)'''
| '''Reactants (Hatree)'''
| '''Product (Hatree)'''
| '''Transition State (Hatree)'''
|'''Energy Barrier (KJ/mol)'''
| '''Reaction Energy(KJ/mol)'''
|-
| '''exo''' || -233.324377 || -267.068644 || -500.393021 || -500.417324 || -500.329164 || 167.65
| 63.84
|-
| '''endo''' || -233.324377 || -267.068644 || -500.393021 || -500.418691 || -500.332149 || 159.82
| 67.40
|-
| colspan=8 |(Note:Values of the sum of electronic and thermal Free Energies, calculation ran at DFT (B3LYP))
|}

The endo product has a more negative energy than the exo product. Therefore it is more thermodinamically stable compare to the exo product.
The energy barrier of the endo product is lower than the exo product. Hence endo product is both kinetically and thermodinamically favourable product.

From table 5, we can see that in the endo HOMO transition state, there are secondary (non-bonding) orbital interactions between the p orbital of oxygens in 1,3-dioxole and the p orbitals in diene. This will lower its energy barrier and make it more kinetically favorable.
The exo product only has a primary (bonding) orbital interactions.Besides that, the sp3 carbon centres of both cyclohexene and 1,3-dioxole might have cause some steric hindrance which cause it to be both unfavourable thermodynamically and kinetically. For the endo product, the sp3 carbon centres of the cyclohexene and 1,3-dioxole are pointing at different direction, hence no steric factors that will cause in increased of energy barrier.

== Exercise 3 ==

== Conclusion ==

== Reference ==
<ref name="bondlength">Bartell, L. S. (1959). Journal of the American Chemical Society, 81(14), 3497–3498. doi:10.1021/ja01523a002</ref>

<ref name="VDW">Batsanov, S. S. (2001). Van der Waals Radii of Elements. Inorganic Materials, 37(9), 871–885. doi:10.1023/A:1011625728803</ref>