ChemWiki - User contributions [en]

Rep:Hrc115ts

2018-01-31T11:33:28Z

Hrc115:

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMOs and LUMOs on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMOs and LUMOs are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high energy reactant HOMO, and dienophile electron poor, providing a low enrgy reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO, decreasing the energy gap between it and the diene LUMO.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2ː Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:31:20Z

Hrc115: /* Computational Methods */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high energy reactant HOMO, and dienophile electron poor, providing a low enrgy reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO, decreasing the energy gap between it and the diene LUMO.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2ː Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:19:13Z

Hrc115: /* Thermochemistry */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high energy reactant HOMO, and dienophile electron poor, providing a low enrgy reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO, decreasing the energy gap between it and the diene LUMO.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2ː Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:16:54Z

Hrc115: /* Molecular Orbitals */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high energy reactant HOMO, and dienophile electron poor, providing a low enrgy reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO, decreasing the energy gap between it and the diene LUMO.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:14:58Z

Hrc115: /* Molecular Orbitals */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:12:21Z

Hrc115: /* Molecular Orbitals */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the reactants make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T11:07:25Z

Hrc115: /* Log Files */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[File:6HRC115_EXOOFB3.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

File:6HRC115 EXOOFB3.LOG

2018-01-31T11:05:55Z

Hrc115:

Rep:Hrc115ts

2018-01-31T11:03:28Z

Hrc115: /* Thermochemistry */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Log Files ==

[[File:2HRC115_ENDOOFB3.LOG]] - endo product

[[Fileː6HRC115_EXOOFB31.LOG]] - exo product

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

File:6HRC115 EXOOFB31.LOG

2018-01-31T11:02:57Z

Hrc115:

File:2HRC115 ENDOOFB3.LOG

2018-01-31T11:02:20Z

Hrc115:

Rep:Hrc115ts

2018-01-31T11:00:43Z

Hrc115: /* TS Vibration */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

== Log Files ==

[[File:HRC115_DAPROD3.LOG]] - optimised product

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

File:HRC115 DAPROD3.LOG

2018-01-31T11:00:27Z

Hrc115:

Rep:Hrc115ts

2018-01-31T10:53:15Z

Hrc115: /* Exercise 3ː Diels-Alder vs Cheletropic */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17. All enrgies are in kJ/mol.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction.<ref>Wiredchemist.com. (2018). Common Bond Energies. [online] Available at: http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html [Accessed 31 Jan. 2018]</ref> In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Log Files ==

[[File:HRC115_SOBER1.LOG]] - exo transition state

[[File:HRC115_NSOFR.LOG]] - endo transition state

[[File:HRC115_CHXBER.LOG]] - cheletropic transition state

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

File:HRC115 CHXBER.LOG

2018-01-31T10:52:50Z

Hrc115:

File:HRC115 NSOFR.LOG

2018-01-31T10:50:29Z

Hrc115:

File:HRC115 NSOB3.LOG

2018-01-31T10:49:57Z

Hrc115:

File:HRC115 SOBER.LOG

2018-01-31T10:48:13Z

Hrc115:

File:HRC115 SOBER1.LOG

2018-01-31T10:39:31Z

Hrc115:

Rep:Hrc115ts

2018-01-31T10:18:26Z

Hrc115: /* Bond Lengths */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.<ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T10:17:43Z

Hrc115: /* Exercise 1ː Reaction of Butadiene with Ethylene */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO-1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A|ref> Bernstein, H. (1961). Bond distances in hydrocarbons. Transactions of the Faraday Society, [online] 57, p.1651. Available at: http://pubs.rsc.org/-/content/articlepdf/1961/tf/tf9615701649 [Accessed 31 Jan. 2018]</ref><ref>Mantina, M., Chamberlin, A., Valero, R., Cramer, C. and Truhlar, D. (2009). Consistent van der Waals Radii for the Whole Main Group. The Journal of Physical Chemistry A, [online] 113(19), pp.5806-5812. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658832/ [Accessed 31 Jan. 2018]</ref>

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T10:08:55Z

Hrc115: /* Computational Methods */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]</ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T10:06:53Z

Hrc115: /* Introduction */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirelɥ.<ref>Hoffmann, R. (1963). An Extended Hückel Theory. I. Hydrocarbons. The Journal of Chemical Physics, [online] 39(6), pp.1397-1412. Available at: https://doi.org/10.1063/1.1734456 [Accessed 31 Jan. 2018]<ref> A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70, 255. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref> However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T09:48:08Z

Hrc115:

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.<ref>Jensen, F. (2007). Introduction to Computational Chemistry. 2nd ed. [ebook] Chichester: John Wiley & Sons Ltd, p.70. Available at: http://karin.fq.uh.cu/qct/books/Jensen_Introduction%20to%20Computational%20Chemistry%202nd%20ed.pdf [Accessed 31 Jan. 2018]</ref>

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

== References ==

{{Reflist}}

Rep:Hrc115ts

2018-01-31T09:37:10Z

Hrc115: Undo revision 659449 by Hrc115 (talk)

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

Rep:Hrc115ts

2018-01-31T09:35:01Z

Hrc115: /* Introduction */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined<ref name="PES" /> <references>.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely<ref name="PM6" /> <references>. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate<ref name="B3LYP" /> <references>. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

Rep:Hrc115ts

2018-01-31T09:30:59Z

Hrc115: /* Diels-Alder vs Cheletropic */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Exercise 3ː Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction, as demonstrated in figure 15.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 15ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure 16.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 16ː Transition state pathways for possible reaction outcomes
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table 2 and figure 17.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre |thumb | Figure 17ː Comparison of rection barriers and energies]]

The endo product has the lowest reaction barrier, but is also the least stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3ː Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table 3 shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

= Conclusion =

The transition states geometries that occur in reactions between butadiene and ethylene, cyclohexadiene and 1,3-dioxole, and xylylene and sulfur dioxide were succesfully found using Gaussview. Those reactions occuring in exercises 1 and 3 were optimised using the PM6 method, and those in exercise 2 were further optimised using the B3LYP method. In exercise 1, the differences in bond lengths throughout the reaction were examined, and when compared to typical carbon bond lengths, they tally with what we would expect. Inspection of molecular orbital energies in exercise 2 reveals that this reaction proceeds with inverse electron demand, and it is the HOMO of the dieneophile that contributes to the new HOMO in the product, rather than the HOMO of the diene. This is because 1,3-dioxole is electron rich (dieneophiles are usually electron poor), which raises its HOMO energy. Exercise 3 shows that despite the endo diels-alder product having the lowest reaction barrier, it is the least stable product. The cheletropic product, which has a high reaction barrier due to its strained transition state geometry, it the most stable as it retains both strong sulfur-oxygen double bonds.

Rep:Hrc115ts

2018-01-31T09:01:38Z

Hrc115: /* The reaction of cyclohexadiene with dioxole */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= Exercise 2ː The reaction of cyclohexadiene with 1,3-dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure 9.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 9: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram, shown in figure 11, was constructed after consideration of the reactant molecular orbitals which are displayed in figure 10.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 10: Molecular orbitals of cyclohexadiene and1,3-dioxole
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 11: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in figures 12 and 13. This becomes even more apparent when the secondary orbitals are considered, as seen in figure 14. There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 12ː Endo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 13ː Exdo transition state molecular orbitals
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 14ː Secondary orbital interactions
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also. These values are shown in table 1.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 1ː reaction barriers and energies for the reaction between cyclohexadiene and 1,3-dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x and figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T08:49:26Z

Hrc115: /* Ex 1ː Reaction of Butadiene with Ethylene */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Exercise 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 2.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 2: Reaction between butadiene and ethylene.]]

Figure 3 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 3ː Molecular orbital diagram of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 3 have been visualised in gaussview and are shown in figure 4.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 4ː Butadiene and ethylene molecular orbitals
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 3. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au. These new molecular orbitals are shown in figure 5, and the transition state molecular orbital diagram is shown in figure 6.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 5ː Transition state molecular orbitals
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 6ː MO TS diagram for reaction between butadiene and ethylene.]]

In figure 6 it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure 7 shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 7ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen, as shown in figure 8.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Figure 8ː Transition State Vibration
! style="background: #ffffff; color: black;" |
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure x.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x and figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T08:39:25Z

Hrc115: /* Introduction */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors. These differences are shown in figure 1.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 1ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some factors entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then optimised to a transition state.

= Ex 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 1.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure x.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x and figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T01:25:48Z

Hrc115: /* Thermochemistry */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Ex 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 1.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure x.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x and figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T01:17:28Z

Hrc115: /* The reaction of cyclohexadiene with dioxole */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Ex 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 1.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product. This is shown in figure x.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115_ex2modiagram.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo HOMO has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

File:Hrc115 ex2modiagram.png

2018-01-31T01:14:46Z

Hrc115:

Rep:Hrc115ts

2018-01-31T01:06:43Z

Hrc115: /* Reaction of Butadiene with Ethylene */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Ex 1ː Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition, shown in figure 1.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of 's' and 'as' correlate to symmetric or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction to be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively, and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius (1.70 A), showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6 -membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T01:04:00Z

Hrc115: /* Introduction */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Computational Methods ==

Gaussview was used for all calculations. The reactants, products, and transition states were optimised (from their drawn configurations on Gaussview to their true structures) by using a PM6 (semi-empirical) method. However, this makes a lot of approximations, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-31T00:04:53Z

Hrc115: /* Molecular Orbitals */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Calculations ==

The reactants, products, and transition states were calculated by using a PM6 (semi-empirical) method. This makes a lot of approximations however, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MOand2.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

File:Hrc115MOand2.png

2018-01-31T00:04:30Z

Hrc115:

Rep:Hrc115ts

2018-01-30T23:41:31Z

Hrc115: /* Transition States */

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using known electron structures, the geometry can be determined.

== Calculations ==

The reactants, products, and transition states were calculated by using a PM6 (semi-empirical) method. This makes a lot of approximations however, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-30T19:35:33Z

Hrc115:

= Introduction =

== Transition States ==

A transition state is the point in a reaction pathway with the highest energy. It is this energy barrier that the reactants must be able to overcome for a reaction to complete, due to factors such as steric hindrance and orbital overlaps. It has no bearing on the stability of the product (when more than one product can result from a reaction) which is determined by its own set of factors.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

In order to be able to determine the geometry of the transition state, the reaction must be considered across a potential energy surface. The transition state is found at a first-order saddle point, and using computational methods, this point is found alongside the molecular geometry.

== Calculations ==

The reactants, products, and transition states were calculated by using a PM6 (semi-empirical) method. This makes a lot of approximations however, uses parameters taken from data, and omits some data entirely. A second method used is the B3LYP (density functional theory) method. This does not make as many approximations and is far more accurate. However these take a long time, so molecules were always first optimised via the PM6 method.

To find the transition states in exercises one and two, a guess transition state was made, optimised to a minimum, and then optimised to a transition state. In the third exercise, first the products were made, bonds were broken, and then minimised to a transition state.

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-30T19:34:32Z

Hrc115: /* Introduction */

= Introduction =

== Transition States ==

== Calculations ==

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable. This was investigated by comparing product energies to the reactants. Further information about the reaction barrier was drawn by contrasting the transition state energies to the reactants also.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

Rep:Hrc115ts

2018-01-30T19:11:53Z

Hrc115: /* Thermochemistry */

Rep:Hrc115ts

2018-01-30T18:47:08Z

Hrc115:

= Introduction =

== Transition States ==

== Calculations ==

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Xylylene ==

Rep:Hrc115ts

2018-01-30T18:41:20Z

Hrc115: /* Reaction Profiles */

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reactions ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Thermochemistry ==

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies
! style="background: #ffffff; color: black;" |Product
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |82.76
| style="background: #ffffff; color: black;" |-98.03
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |86.75
| style="background: #ffffff; color: black;" |-98.68
|-
| style="background: #ffffff; color: black;" |cheletropic
| style="background: #ffffff; color: black;" |105.08
| style="background: #ffffff; color: black;" |-154.99
|}

[[File:Hrc115_reactionprofileex3.png|550px|centre]]

The endo product has the lowest reaction barrier, but is also the less stable product. The cheletropic reaction has the highest reaction barrier, but is the most stable product due to bond energies.
{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Bond strengths
! style="background: #ffffff; color: black;" |Bond
! style="background: #ffffff; color: black;" |Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | C-O
| style="background: #ffffff; color: black;" |358
|-
| style="background: #ffffff; color: black;" |C-S
| style="background: #ffffff; color: black;" |272
|-
| style="background: #ffffff; color: black;" |C=S
| style="background: #ffffff; color: black;" |522
|}

Table x shows the bond strengths relevant to this reaction. In the diels-alder reactions, new C-O and C-S bonds are formed, and there is a loss of one S=O double bond. The cheletropic involves the formation of two new C-S bonds. Despite the C-O bonds being stronger than the C-S, the diels-alder product involves the loss of a very strong S=O double bond. This overrides the reaction energies, making the cheletropic product more stable. However, it has the highest reaction barrier as it has the most twisted and strained transition state, due to having a smaller ring size than the diels-alder.

Xylylene is a very unstable molecule. Looking at the IRC pathways, as soon as the sulfur dioxide approaches, but before it bonds, xylylene changes its bonding character to become aromatic, a much more stable structure.

== Xylylene ==

File:Hrc115 reactionprofileex3.png

2018-01-30T18:05:08Z

Hrc115:

File:Hrc115 reactionprofile.png

2018-01-30T18:04:21Z

Hrc115: Hrc115 uploaded a new version of File:Hrc115 reactionprofile.png

File:Hrc115 reactionprofile.png

2018-01-30T18:03:56Z

Hrc115: Hrc115 uploaded a new version of File:Hrc115 reactionprofile.png

Rep:Hrc115ts

2018-01-30T17:57:12Z

Hrc115: /* Reaction Profiles */

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reaction Profiles ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

The pathway of the transition states for each outcome is illustrated in figure x.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

An examination of thermochemistry provides information on the different energies, and therefore preferred products. This is shown in table x andfigure x.

[[File:Hrc115 reactionprofile.png|550px|centre]]

== Xylylene ==

Rep:Hrc115ts

2018-01-30T17:54:07Z

Hrc115: /* Diels-Alder vs Cheletropic */

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

== Reaction Profiles ==

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

[[File:Hrc115 reactionprofile.png|550px|centre]]

== Xylylene ==

Rep:Hrc115ts

2018-01-30T17:53:15Z

Hrc115: /* Secondary Orbital Interactions */

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

= Diels-Alder vs Cheletropic =

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Reaction Profile ==

[[File:Hrc115 reactionprofile.png|550px|centre]]

== Xylylene ==

Rep:Hrc115ts

2018-01-30T17:52:50Z

Hrc115: /* Thermochemistry */

= Reaction of Butadiene with Ethylene =

== Molecular Orbitals ==

The reaction between ethylene and butadiəne is a [4+2] cycloaddition.

[[File:Hrc115scheme1.png|center|600px|thumb| Figure 1: Reaction between butadiene and ethylene.]]

Figure 2 shows an MO diagram for the two reactant including the HOMO and LUMO on each. The energies (in au.) for each set of orbitals have been calculated in Gaussview. The labels of s and as correlate to symmetrical or anti-symmetric orbitals respectively.

[[File:Hrc115MO1.png|center|500px |thumb| Figure 2ː Molecular orbitals of butadiene (left) and ethylene (right). ]]

The HOMO's and LUMO's on each molecule shown in figure 2 have been visualised in gaussview and are shown below.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Butadiene HOMO
! style="background: #ffffff; color: black;" | Butadiene LUMO
! style="background: #ffffff; color: black;" | Ethylene HOMO
! style="background: #ffffff; color: black;" | Ethylene LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 11; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 12; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>CIS1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 6; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 2; mo 7; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>ETH1POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

There are two HOMO-LUMO interactions shown as 1 and 2 in figure 2. It can be seen that the symmetric HOMO interacts with the symmetric LUMO, and this also holds true for the anti-symmetric orbitals. From this it is possible to draw the conclusion that interacting orbitals must be of the same symmetry for a reaction be allowed, otherwise it would be forbidden. The orbital overlap integral would then have a value of zero for symmetric - anti-symmetric interactions (meaning that there are no orbitals overlapping) and non-zero for a symmetric - symmetric or anti-symmetric - anti-symmetric overlap (corresponding to some degree of overlap). These four orbitals on the products make four new orbitals in the transition state, a new HOMO and LUMO, one with an energy lower than the HOMO (HOMO - 1), and one with an energy higher than the LUMO (LUMO + 1). An observation of the new orbitals formed in Gaussview reveals that interaction 2 leads to the new HOMO and LUMO, and 1 creates the orbitals on either side of these. This can also be seen from the energy differences between the orbitals, as the combination with the smaller difference leads to the new HOMO and LUMO. Interaction 1 has an energy difference of 0.40331 au, and 2 of 0.39424 au.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Product HOMO-1
! style="background: #ffffff; color: black;" | Product HOMO
! style="background: #ffffff; color: black;" | Product LUMO
! style="background: #ffffff; color: black;" | Product Lumo + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 16; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 17; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 18; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 16; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>HRC115_DABERNYPOP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

[[File:Hrc115ex1fullmo2.png|center | 600px |thumb| Figure 3ː MO TS diagram for reaction between butadiene and ethylene.]]

In this MO diagram, it shows that the new HOMO is higher in energy than the ethylene HOMO from which it is partly comprised. This is because it is the MO diagram of a transition state, which is the highest energy point in the reaction pathway. This is the activation energy which must be overcome to reach the products.

== Bond Lengths ==

Figure four shows the changes in bond lengths that occur throughout the reaction. Lengths are given in Angstroms. The typical sp3 and sp2 bond lengths are 1.54 A and 1.34 A respectively. and the van der Waal's radius- half of the smallest possible length between two non-bonded atoms- is 1.70 A.

[[File:Hrc115 l.png|center|800px| thumb |Figure 4ː Changes in bond lengths throughout the reaction]]

Upon going from the reactants to the transition state, the double bonds lengthen and single shortens. As the reaction then proceeds to the products, the new double bond mirrors the length of those found in the products. The single bonds are all longer than that one seen in the butadiene, with those adjacent to the new double bond slightly shorter than the others. This is due to the product having an overall less sp2 character than the reactants. In the transition state, all the bond lengths exist between the lengths of those of typical sp3 and sp2 carbon-carbon bonds- the transition state shows an intermediate where the bonds exist as though between states and is not a stable product. The distance between carbons 1 & 6, and 4 & 5, which will become bonded in the product, are observed to be 2.11 A. This is longer than the van der Waal's radius, showing that the atoms are still far apart enough to not need to be bonded. This also helps to prove the structure found is indeed the transition state as the 6- membered ring is yet to be formed.

== TS Vibration ==

When the imaginary vibration of the transition state is animated, the movement corresponding to the reaction pathway at this point can be seen.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | Transition State Vibration
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>500</size>
<uploadedFileContents>HRC115_DABERNY.LOG</uploadedFileContents>
<script>frame 17; vibration 1;rotate x -20; </script>
</jmolApplet>
</jmol>
|}

The distance between the two pairs of terminal atoms reduces at the same rate. This shows that the reaction proceeds via a concerted mechanism, where all new bonds are formed at the same time.

= The reaction of cyclohexadiene with dioxole =

== Molecular Orbitals ==

The reaction between cyclohexadiene and 1,3-dioxole is also a [4+2] cycloaddition. However in this case, two different stereoisomers may be synthesised; an endo or an exo product.

[[File:Hrc115_ex2scheme.png|center|300px |thumb | Figure 5: Reaction between cyclohexadiene and 1,3-dioxole.]]

An MO diagram was constructed after consideration of the reactant molecular orbitals which are shown in table 2.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 2: Molecular Orbitals of Reactants
! style="background: #ffffff; color: black;" | Cyclohexadiene HOMO
! style="background: #ffffff; color: black;" | Cyclohexadiene LUMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole HOMO
! style="background: #ffffff; color: black;" | 1,3-Dioxole LUMO
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 22; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 6; mo 23; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115_HEXAOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 19; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 12; mo 20; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 DIOXOFB3POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

As for the previous reaction, the new HOMO's and LUMO's are formed from the 1,3-dioxole HOMO and cyclohexadiene LUMO, as this pairing has the smaller energy difference (0.32545 au vs 0.3304). It is much more common in diels-alder reactions for the new HOMO and LUMO to be generated from the diene HOMO and dienophile LUMO. This is due to inverse electron demand. Usually the diene is electron rich, providing a high reactant HOMO, and dienophile electron poor, providing a low reactant LUMO. However in this situation, the dienophile is electron rich due to the adjacent oxygens, which donate electron density to the double bond. This raises the energy of its HOMO. Despite this anomaly, the reaction still obeys the Woodward-Hoffman rules so is thermally allowed and proceeds.

[[File:Hrc115 ex2mo.png|center|500px |thumb| Figure 6: Molecular orbital diagram for the endo and exo transition state.]]

Comparison of the transition states show the endo one has a slightly lower energy. This is because in the transition state the endo configuration has a much greater overlap between diene and dienophile, leading to stabilising interactions between the MO's. This is illustrated in tables 3 and 4. This becomes even more apparent when the secondary orbitals are considered (table 5). There are large regions of overlap in the endo transition state in comparison to the exo.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 3: Molecular Orbitals of Endo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 4: Molecular Orbitals of Exo Transition State
! style="background: #ffffff; color: black;" | HOMO - 1
! style="background: #ffffff; color: black;" | HOMO
! style="background: #ffffff; color: black;" | LUMO
! style="background: #ffffff; color: black;" | LUMO + 1
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 40; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 42; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 43; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 5: Secondary Orbital Interactions in HOMO of Exo and Endo Transition State
! style="background: #ffffff; color: black;" | ENDO TS
! style="background: #ffffff; color: black;" | EXO TS
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

== Thermochemistry ==

Information about the kinetic and thermodynamic products of the reaction can be gained by examining the thermochemistry. Although the HOMO of the endo transition state is lower in energy it does not reveal which product is energetically more favourable.

[[File:Hrc115_profile.png | 500px | centre | thumb | Figure 7ː Reaction barrier and energy ]]

To do this the energy of the products must be compared to the reactants. This difference is called the reaction energy. The energy of the transition state was also compared to the reactants, to further examine the reaction barrier.

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Reaction Barriers and Energies for the Reaction Between Cyclohexadiene and 1,3-Dioxole
! style="background: #ffffff; color: black;" |Stereoisomer
! style="background: #ffffff; color: black;" |Reaction Barrier / kJ/mol
! style="background: #ffffff; color: black;" |Reaction Energy / kJ/mol
|-
| style="background: #ffffff; color: black;" | endo
| style="background: #ffffff; color: black;" |158.64
| style="background: #ffffff; color: black;" |-66.09
|-
| style="background: #ffffff; color: black;" |exo
| style="background: #ffffff; color: black;" |166.34
| style="background: #ffffff; color: black;" |-62.61
|}

The endo stereoisomer has both a lower reaction barrier and reaction energy. This means that not only is it formed more easily, but its product is also more stable. The lower reaction barrier is due to the previously discussed secondary orbital interactions. The fact it is a more stable product can be explained due to sterics. The oxygen-carbon-oxygen fragment in the exo product could be experiencing hindrance from the bridging carbons, which do not exist in the endo product as it is facing downwards.

== Secondary Orbital Interactions ==

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
! style="background: #ffffff; color: black;" | ENDO TS Secondary Orbital Interactions
! style="background: #ffffff; color: black;" | EXO TS Secondary Orbital Interactions
|-
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 8; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>2HRC115 2B31POP.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
| <jmol>
<jmolApplet>
<color>white</color>
<size>250</size>
<script>frame 18; mo 41; mo nodots nomesh fill translucent; mo titleformat ""; set antialiasdisplay on; mo cutoff 0.01</script>
<uploadedFileContents>6HRC115 EXOB3POP OTHER.LOG</uploadedFileContents>
</jmolApplet>
</jmol>
|}

= Diels-Alder vs Cheletropic =

The reaction between sulfur dioxide and xylylene can either proceed as a hetero-diels-alder (producing either an endo or exo product) or as a cheletropic reaction.

[[File:Hrc115_ex3scheme.png |centre| 500px| thumb| Figure 6ː Scheme for the reaction between xylylene and sulfur dioxide.]]

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none;"
|+ Table 6ː IRC's of Reactopm
! style="background: #ffffff; color: black;" | Endo
! style="background: #ffffff; color: black;" | Exo
! style="background: #ffffff; color: black;" | Cheletropic
|-
| [[File:Hrc115_endos.gif]]
| [[File:Hrc115_exos.gif]]
| [[File:Hrc115_chs1.gif]]
|}

== Reaction Profile ==

[[File:Hrc115 reactionprofile.png|550px|centre]]

== Xylylene ==